Estimates of mass absorption cross sections of black carbon for filter-based absorption photometers in the Arctic

Long-term measurements of atmospheric mass concentrations of black carbon (BC) are needed to investigate changes in its emission, transport, and deposition. However, depending on instrumentation, parameters related to BC such as aerosol absorption coefficient (b_abs) have been measured instead. Most ground-based measurements of b_abs in the Arctic have been made by filter-based absorption photometers, including particle soot absorption photometers (PSAPs), continuous light absorption photometers (CLAPs), Aethalometers, and multi-angle absorption photometers (MAAPs). The measured b_abs can be converted to mass concentrations of BC (M_BC) by assuming the value of the mass absorption cross section (MAC; M_BC= $b_{\mathrm{abs}}/$ MAC). However, the accuracy of conversion of b_abs to M_BC has not been adequately assessed. Here, we introduce a systematic method for deriving MAC values from b_abs measured by these instruments and independently measured M_BC. In this method, M_BC was measured with a filter-based absorption photometer with a heated inlet (COSMOS). COSMOS-derived M_BC (M_BC (COSMOS)) is traceable to a rigorously calibrated single particle soot photometer (SP2), and the absolute accuracy of M_BC (COSMOS) has been demonstrated previously to be about 15 % in Asia and the Arctic. The necessary conditions for application of this method are a high correlation of the measured b_abs with independently measured M_BC and long-term stability of the regression slope, which is denoted as MAC_cor (MAC derived from the correlation). In general, b_abs–M_BC (COSMOS) correlations were high (r²= 0.76–0.95 for hourly data) at Alert in Canada, Ny-Ålesund in Svalbard, Barrow (NOAA Barrow Observatory) in Alaska, Pallastunturi in Finland, and Fukue in Japan and stable for up to 10 years. We successfully estimated MAC_cor values (10.8–15.1 m² g⁻¹ at a wavelength of 550 nm for hourly data) for these instruments, and these MAC_cor values can be used to obtain error-constrained estimates of M_BC from b_abs measured at these sites even in the past, when COSMOS measurements were not made. Because the absolute values of M_BC at these Arctic sites estimated by this method are consistent with each other, they are applicable to the study of spatial and temporal variation in M_BC in the Arctic and to evaluation of the performance of numerical model calculations.

1 Introduction

Black carbon (BC) aerosols strongly absorb solar radiation and thereby impact the radiation budget in the Arctic (Bond et al., 2013; AMAP, 2015). In addition, BC deposited on snow decreases the snow surface albedo and accelerates snowmelt (AMAP, 2015; Flanner et al., 2009). According to recent climate model calculations in the sixth phase of the Coupled Model Intercomparison Project (CMIP6; Eyring et al., 2016), BC contributes the second largest positive radiative forcing in the Arctic, after carbon dioxide (CO₂) (Oshima et al., 2020). BC is one of the short-lived climate forcers (SLCFs), and reductions of BC emissions can decrease the positive Arctic radiative forcing over much shorter timescales than reductions of CO₂ emissions can (Sand et al., 2016). Long-term measurements of mass concentrations of BC in the atmosphere (M_BC [µg m⁻³]) at various locations provide fundamental data for the detection of long-term trends in M_BC in the Arctic that are associated with changes in BC emissions. Such M_BC data are also useful for validation and improvement of climate models. However, because many long-term surface instruments measure aerosol light absorption coefficient (b_abs [Mm⁻¹]) rather than M_BC, there are large uncertainties in M_BC estimated from the measurements of b_abs; these uncertainties have not been critically evaluated.

A continuous soot monitoring system called COSMOS (Kanomax, Osaka, Japan) has been developed to measure M_BC (Miyazaki et al., 2008; Kondo et al., 2009, 2011). This filter-based absorption photometer is equipped with an inlet that is heated to 300 ^∘C to remove non-refractory components from the aerosol phase. COSMOS M_BC values (M_BC (COSMOS)) have been compared with those measured by a single particle soot photometer (SP2; Droplet Measurement Technologies, Longmont, CO, USA; M_BC (SP2)), which is based on a laser-induced incandescence technique (Schwarz et al., 2006; Moteki and Kondo, 2010); simultaneous measurements in Asia and at Ny-Ålesund in Svalbard have shown that M_BC (SP2) and M_BC (COSMOS) agree to within about 10 % (Kondo et al., 2009, 2011; Ohata et al., 2019).

Long-term measurements of b_abs at various sites have been carried out by other types of filter-based absorption photometers, including the particle absorption soot photometer (PSAP; Radiance Research, Seattle, WA, USA), the continuous light absorption photometer (CLAP; NOAA, Boulder, CO, USA; Ogren et al., 2017), the Aethalometer (Magee Scientific, Berkeley, CA, USA), and the multi-angle absorption photometer (MAAP; Thermo Scientific, Waltham, MA, USA) (e.g., Schmeisser et al., 2018). Measurements of light-absorbing and light-scattering properties of aerosols are important for constraining their interannual and seasonal variability, potential particle sources, and resulting aerosol–radiation interactions in the Earth system (Schmeisser et al., 2018; Bellouin et al., 2020). However, the accuracy and stability of conversion of b_abs obtained by these instruments to M_BC have not yet been fully evaluated, mainly because of a lack of simultaneous and reliable long-term M_BC measurements. The relationship between b_abs obtained by these instruments and M_BC is complicated by complex contributions from mixing states of BC (i.e., lensing effect by BC-coating materials; Bond et al., 2006: Lack et al., 2008), other co-existing light-absorbing aerosols such as brown carbon and mineral dust, and measurement artifacts by light-scattering aerosols on filters (Bond et al., 1999). Evaluations that have been completed to date include those of Kanaya et al. (2013, 2020), who compared M_BC (COSMOS) with the b_abs measured by MAAP (b_abs (MAAP)) on Fukue Island, Japan, and Sinha et al. (2017), who compared b_abs measured by PSAP (b_abs (PSAP)) at NOAA Barrow Observatory near Utqiaġvik, Alaska and Ny-Ålesund (Zeppelin station), Svalbard. The results of these studies showed that b_abs (MAAP) and b_abs (PSAP) were strongly correlated with M_BC (COSMOS), making it possible to convert b_abs to M_BC at these sites with reasonable accuracy. Long-term observations of b_abs have also been made in the Arctic: Alert in Canada by PSAP and Aethalometer (Sharma et al., 2004, 2006, 2017), Ny-Ålesund by Aethalometer (Eleftheriadis et al., 2009) and MAAP, and Pallastunturi in Finland by MAAP (Hyvärinen et al., 2011; Lihavainen et al., 2015). To investigate the possibility of converting b_abs to M_BC at each of these sites, it is important to simultaneously measure M_BC and b_abs by collocating a COSMOS (or SP2) at each site with each of these filter-based absorption photometer instruments.

The conversion of b_abs obtained by these instruments to M_BC can be made by assuming a reasonable conversion factor, i.e, the value of mass absorption cross section (MAC [m² g⁻¹]; M_BC= b_abs/MAC). The MAC values can depend on location because the spatiotemporal variations in microphysical properties of BC (i.e., mixing states and size distributions) and properties of co-existing light-absorbing and light-scattering aerosols will affect b_abs measurements. The plausible MAC values for conversion can also depend on the type of instrument because each instrument uses a different wavelength or wavelengths and adopts various correction methods for quantifying b_abs. Despite several intercomparisons and field experiments (Asmi et al., 2021) as well as thorough assessment of these techniques (Lack et al., 2008; Moosmüller et al., 2009), the simultaneous changes in aerosol source region, mixing state, concentration, and particle optical size are reflected in the instruments' response in a complex way and with a variable level of uncertainty.

In general, the MAC of BC, here simply denoted as “MAC_BC” for both bare and internally mixed BC, is a fundamental optical parameter that relates M_BC with b_abs of BC (b_abs,BC) in climate models (i.e., $b_{\mathrm{abs},\mathrm{BC}}=M_{\mathrm{BC}}$ × MAC_BC). Bond and Bergstrom (2006) reported the MAC_BC value of 7.5 m² g⁻¹ at a wavelength of 550 nm for combusted fresh BC. Cho et al. (2021) estimated MAC_BC values of 6–12 m² g⁻¹ at 550 nm in the Asian outflow using aircraft-based SP2 data and Mie theory. Yuan et al. (2021) showed that the MAC_BC values at 870 nm at a rural site in Germany clearly increased as the coating thickness of BC increased.

However, in this paper we focus on the MAC values mainly from the viewpoint of a conversion factor to obtain error-constrained M_BC from the b_abs measurements by the filter-based absorption photometers because such M_BC data will be the observational base for understanding long-term trends and spatial distributions of BC in the Arctic. Detailed investigations of the accuracy of the absolute values of b_abs measured at each site are beyond the scope of this study.

We critically re-examine the concepts underpinning the use of filter-based instruments to estimate M_BC. We derive MAC values for PSAP–CLAP, Aethalometer, and MAAP measurements based on their comparison with COSMOS measurements at the four abovementioned Arctic sites (Alert, Ny-Ålesund, Barrow, and Pallastunturi) and one East Asian site (Fukue). The variability of the derived MAC values and their dependencies on observation site and instrument type are analyzed. We also compare M_BC values measured by COSMOS and SP2 at Alert and Fukue to confirm their agreement under different environmental conditions.

2 Methods

2.1 Observation sites

Measurements of b_abs by the various types of filter-based absorption photometers were compared with measurements of M_BC by COSMOS at Arctic sites Alert in Canada (82.5^∘ N, 62.5^∘ W; Sharma et al., 2017), Ny-Ålesund (Zeppelin station) in Svalbard (78.9^∘ N, 11.9^∘ E; Sinha et al., 2017), Barrow (NOAA Barrow Observatory) in Alaska (71.3^∘ N, 156.6^∘ W; Sinha et al., 2017), and Pallastunturi (Pallas, hereafter) in Finland (68.0^∘ N, 24.0^∘ E; Hyvärinen et al., 2011), as summarized in Table 1 and Fig. 1. Along with these sites, comparisons were also made at a remote site on Fukue Island (32.8^∘ N, 128.7^∘ E; Kanaya et al., 2020) in Japan, where air masses from the Asian continent are occasionally transported to the site and properties of aerosols should be distinctly different from those at the Arctic sites. Instruments used at each site are listed in Table 1 and described in the following section. Note that measurements at NOAA Barrow Observatory near Utqiaġvik are referred to as measurements at Barrow, using the name of the measurement site hereafter.

Table 1 Observation sites, periods, and instruments used in this study.

Figure 1 Locations of the Arctic sites where M_BC and b_abs were measured for this study.

2.2 Instruments

2.2.1 SP2

In this study we used the SP2 and COSMOS as standard instruments to measure M_BC. 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 (D_m) 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 M_BC (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.

2.2.2 COSMOS

Measurements of M_BC by COSMOS

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

$$\begin{array}{}\text{(1)}& b_{\mathrm{abs}}\left(\mathrm{COSMOS}\right)=f_{\mathrm{fil}}{b}_{\mathrm{0}}.\end{array}$$

Here, f_fil is a factor used to correct for the increase in absorption caused by multiple scattering in the filter medium. It is given by

$$\begin{array}{}\text{(2)}& f_{\mathrm{fil}}\left(\mathrm{Tr}\right)={\displaystyle \frac{\mathrm{1}}{[\mathrm{1.0796}\mathrm{Tr}+\mathrm{0.71}]B}}\text{with}\mathrm{Tr}\ge \mathrm{0.7},\end{array}$$

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

$$\begin{array}{}\text{(3)}& \mathrm{MAC}\left(\mathrm{COSMOS},\mathrm{SP}\mathrm{2}\right)\equiv {\displaystyle \frac{b_{\mathrm{abs}}\left(\mathrm{COSMOS}\right)}{M_{\mathrm{BC}}\left(\mathrm{SP}\mathrm{2}\right)}},\end{array}$$

where the numerator and denominator, respectively, are simultaneous measurements of b_abs [Mm⁻¹] by COSMOS and M_BC [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, M_BC (COSMOS) [g m⁻³] at standard temperature and pressure (0 ^∘C, 1013 hPa) can be estimated as

$$\begin{array}{}\text{(4)}& M_{\mathrm{BC}}\left(\mathrm{COSMOS}\right)={\displaystyle \frac{b_{\mathrm{abs}}\left(\mathrm{COSMOS}\right)}{\mathrm{MAC}\left(\mathrm{COSMOS},\mathrm{SP}\mathrm{2}\right)}}.\end{array}$$

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 b_abs (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 M_BC, not b_abs. In this sense, M_BC (COSMOS) is different from “equivalent” BC mass concentrations estimated from the unheated b_abs 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 b_abs (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 b_abs (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 M_BC (COSMOS).

It is important to compare M_BC (COSMOS) and M_BC (SP2) outside Tokyo and Osaka, to confirm both the strong correlation between M_BC (COSMOS) and M_BC (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. M_BC (COSMOS) and M_BC (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, M_BC, 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 M_BC (COSMOS) were about 10 % based on the range of agreement between M_BC 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 M_BC (COSMOS) to be about 15 %, including the abovementioned 10 % uncertainty of M_BC (SP2). This 15 % uncertainty also covers the range of agreement between M_BC (COSMOS) and M_BC (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 M_BC in this study, thermal–optical analysis, which quantifies elemental carbon (EC) mass concentrations (M_EC), has also been a traditional standard method to measure BC. Measurements of M_EC can depend on the temperature protocol and optical charring correction method used (e.g., Bond et al., 2013). Agreements within 10 % of M_BC (SP2), M_BC (COSMOS), and M_EC were reported by Kondo et al. (2011), whereas systematic differences between M_BC (SP2) and M_EC up to a factor of 2 were found by Pileci et al. (2021). Although the difference between M_BC (COSMOS) and M_EC 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 (M_BC (COSMOS) <20 ng m⁻³). Considering these previously reported agreements and discrepancies between M_BC (SP2 or COSMOS) and M_EC, in some cases the MAC values determined by b_abs and M_BC measurements (this study) can differ from those determined by b_abs and M_EC measurements (Zanatta et al., 2016).

Effect of light-absorbing FeO_x particles on M_BC (COSMOS)

Light-absorbing iron oxide (FeO_x) aerosols such as magnetite, which the SP2 can distinguish from BC (Yoshida et al., 2016; Lamb, 2019), can affect M_BC measured by filter-based absorption photometers. FeO_x 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 (D_m= 70–850 nm for BC and D_m = 170–2100 nm for FeO_x), the mass concentration ratios of FeO_x 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). FeO_x 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 FeO_x on M_BC measured by the COSMOS. The ratio of light absorbed by FeO_x to that absorbed by BC at a wavelength λ (ε(λ)) is given by

$$\begin{array}{}\text{(5)}& \mathit{\epsilon }\left(\mathit{\lambda }\right)={\displaystyle \frac{{\int }_{D_{\mathrm{L}}}^{D_{\mathrm{U}}}\frac{\mathrm{d}{M}_{{\mathrm{FeO}}_x}}{\mathrm{dlog}{D}_{\mathrm{m}}}{\mathrm{MAC}}_{\mathrm{Mie}\mathrm{\_}\mathrm{FeOx}}\left(D_{\mathrm{m}},\mathit{\lambda }\right)\mathrm{dlog}{D}_{\mathrm{m}}}{{\int }_{D_{\mathrm{L}}}^{D_{\mathrm{U}}}\frac{\mathrm{d}{M}_{\mathrm{BC}}}{\mathrm{dlog}{D}_{\mathrm{m}}}{\mathrm{MAC}}_{\mathrm{Mie}\mathrm{\_}\mathrm{BC}}\left(D_{\mathrm{m}},\mathit{\lambda }\right)\mathrm{dlog}{D}_{\mathrm{m}}}},\end{array}$$

where D_m is mass-equivalent diameter of bare BC or FeO_x; D_L and D_U are the lower and upper limits, respectively, of the diameter for the integral calculus; d$M_{\mathrm{BC}}/$ dlogD_m and d$M_{{\mathrm{FeO}}_x}/$ dlogD_m are the mass size distributions of BC and FeO_x, respectively; and MAC_{Mie_BC} (D_m, λ) and MAC_{Mie_FeOx} (D_m, λ) are the MAC values of bare BC and FeO_x, respectively, for D_m and λ calculated by Mie theory.

The mass size distributions of BC and FeO_x 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 MAC_{Mie_BC} (D_m, λ) and MAC_{Mie_FeOx} (D_m, λ) data (Fig. 2) were calculated by Mie theory for λ= 565 nm (wavelength used for COSMOS). For this calculation, we assumed BC and FeO_x 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 FeO_x we used was 2.56 + 0.57i, which is the value for magnetite at λ= 600 nm (Huffman and Stapp, 1973).

Figure 2 Mass size distributions of BC (black line) and FeO_x (red line) and mass absorption cross sections calculated by Mie theory for bare BC (black dashed line) and bare FeO_x (red dashed line) at (a) Fukue in April 2019 and (b) Ny-Ålesund in March 2017. D_m is the mass-equivalent diameter of bare BC or FeO_x. Assumptions for the Mie calculations are given in Sect. 2.

From Eq. (4), the ε values at Fukue and Ny-Ålesund were calculated to be 3.6 % and 1.9 %, respectively, for (D_L, D_U)= (30, 1000 nm). These ε values became 4.6 % and 2.6 % for (D_L, D_U)= (30, 2500 nm). Because COSMOS is equipped with a PM₁ cyclone, we estimated the effect of light absorption by FeO_x on M_BC 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 FeO_x because the PM₁ cyclone is designed to remove particles of >1 µm aerodynamic diameter (D_a). Due to the fractal shape and high density of FeO_x particles (Moteki et al., 2017), D_m is considerably smaller than D_a for FeO_x particles, and thus D_U in Eq. (4) should be less than 1 µm.

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

The effect of FeO_x on b_abs may be somewhat higher for the other filter-based absorption photometers than for COSMOS if they are equipped with a larger particle size cut (PM_2.5 or PM₁₀). For accurate measurements of M_BC, the use of a PM₁ cyclone or impactor is recommended to minimize the effects of FeO_x, as well as other refractory particles such as natural dust and sea-salt particles.

2.2.3 Filter-based absorption photometers other than COSMOS

PSAP and CLAP

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 b_abs 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 b_abs (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 b_abs for the PSAP or CLAP (hereafter, b_abs (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 b_abs 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.

Aethalometer

An AE-31 Aethalometer (Hansen et al., 1984) has been used for measurements of b_abs 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 b_abs (Aethalometer) from ATN data, the correction factor C_f= 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 C_f 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 C_f at an attenuation value of 80. These uncertainties are considered small compared to the overall b_abs 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 $\mathrm{14}\mathrm{625}/$ (λ [nm] ×C₀) [m² g⁻¹], which corresponds to 7.1 m² g⁻¹ for λ = 590 nm and C₀= 3.5.

MAAP

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, b_abs (MAAP) from particles deposited on the filter is derived by radiative transfer calculations. The uncertainty of b_abs (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 b_abs (MAAP) and M_BC measured at four sites in Germany by the German reference method VDI2465 Part 1 (GRM; Schmid et al., 2001), represented by

$$\begin{array}{}\text{(6)}& \mathrm{MAC}\left(\mathrm{MAAP},\mathrm{GRM}\right)\equiv {\displaystyle \frac{b_{\mathrm{abs}}\left(\mathrm{MAAP}\right)}{M_{\mathrm{BC}}\left(\mathrm{GRM}\right)}}.\end{array}$$

For the measurements of M_BC (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 M_BC (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 M_BC, 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).

3 Results and discussion

3.1 Alert

3.1.1 COSMOS–SP2 comparison

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 M_BC (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 M_BC (COSMOS) and M_BC (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 M_BC ranges observed, the agreement between M_BC (COSMOS) and M_BC (SP2) at Alert was generally within 10 %. The degree of agreement between M_BC (COSMOS) and M_BC (SP2) was also examined on a logarithmic scale in Fig. S1a in the Supplement. When M_BC (SP2) is relatively low (M_BC <10 ng m⁻³), which corresponds to the monthly-averaged M_BC ranges in summer at Arctic sites (Sinha et al., 2017), M_BC (COSMOS) tended to be higher than M_BC (SP2) by about 1–2 ng m⁻³. This small absolute difference is consistent with the previously reported difference between M_BC (COSMOS) and M_EC at Barrow (Sinha et al., 2017).

Figure 3 (a) Number and mass size distributions of BC averaged over the observation period at Alert from January to May 2018. The dashed (solid) red line is the lognormal fit to the number (mass) size distribution. (b) Time series (1 h data) and (c) correlation of M_BC measured by COSMOS and SP2. The solid red line in the correlation plot is the least-squares regression forced through the origin.

Although this agreement between M_BC (COSMOS) and M_BC (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 M_BC (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 (ρ_eff) 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 ρ_eff 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 ρ_eff (= 0.7 g cm⁻³) for Aquadag was assumed in order to derive M_BC (SP2) at Alert. However, we have found that M_BC (SP2) at Alert was highly dependent on the assumed ρ_eff 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 M_BC (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 (D_m ∼ 600 nm) was lower than that for the UT-SP2 (D_m ∼ 850 nm), although the abovementioned extrapolation up to 1000 nm was made to derive M_BC (SP2) at Alert. Despite these differences between EC-SP2 and UT-SP2, M_BC (COSMOS) and M_BC (SP2) agree to within 10 % at Alert, consistent with previous studies that reported the stability of the relationship between M_BC (COSMOS) and M_BC (SP2) at various sites (Kondo et al., 2011; Ohata et. al., 2019).

3.1.2 COSMOS–PSAP comparison

Measurements of M_BC (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 M_BC (COSMOS) were strongly correlated with b_abs (PSAP; λ = 550 nm) for 2018–2019 (r² ∼ 0.96; Fig. 4a–d). In this study, we define the MAC value, MAC_cor, as the slope of the least-squares regression forced through the origin in the correlation plot. The values of MAC_cor (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 b_abs, 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.

Table 2 MAC_cor (PSAP–CLAP; λ) values at Alert during 2018–2019. r² is the square of the correlation coefficient.

Figure 4 Time series of M_BC (COSMOS) and b_abs (PSAP; λ= 550 nm) from January 2018 to December 2019 at Alert for (a) 1 h averaged and (b) 24 h averaged data. (c, d) Corresponding correlations of M_BC (COSMOS) and b_abs (PSAP). The solid red lines are the least-squares regressions forced through the origin. (e, f) Corresponding histograms of b_abs (PSAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³. The interquartile ranges are shown in parentheses.

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

Table 3 MAC, r², and variability of MAC (V_MAC; interquartile range in relative terms) of MAAP, PSAP–CLAP, and Aethalometer at observation sites in this study.

^a Total suspended particles. ^b A PM_2.5 cyclone was used before November 2011.

3.1.3 COSMOS–Aethalometer comparison

Measurements of b_abs 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 b_abs (Aethalometer; λ= 590 nm) and M_BC (COSMOS) in 2018–2019 are shown in Fig. S3a and b in the Supplement. b_abs (Aethalometer; λ= 590 nm) was highly correlated (r²>0.90) with M_BC (COSMOS) (Fig. 5a and b). The MAC_cor (Aethalometer; λ= 590 nm) values were 12.5 and 12.7 m² g⁻¹ for the 1 and 24 h data, respectively. The MAC_med values of the b_abs (Aethalometer) $/$ M_BC (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 MAC_cor values to within 8 %. Therefore, depending on the MAC values used, the estimated M_BC values can differ by about 8 %. Because the interquartile ranges of the b_abs (Aethalometer) $/M_{\mathrm{BC}}$ (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 V_MAC was about 22 % (with an M_BC threshold of 2 ng m⁻³) for b_abs (Aethalometer; λ= 590 nm) at Alert (Table 3). The MAC_med values for low M_BC data (M_BC (COSMOS) <10 ng m⁻³) agree with those for all datasets to within 10 % (Fig. S3c and d in the Supplement).

Figure 5 Correlations of M_BC (COSMOS) and b_abs (Aethalometer; λ= 590 nm) from January 2018 to December 2019 at Alert for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (Aethalometer) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

The MAC_cor (Aethalometer) values for each wavelength are summarized in Table 4. Note that these wavelength-dependent MAC_cor values should be interpreted as the simple conversion factors to obtain average M_BC from b_abs (Aethalometer), which might have been contributed to by BC and also other light-absorbing aerosols. In other words, these MAC_cor values differ from MAC_BC, 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 b_abs (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 MAC_cor (Aethalometer) and MAC_cor (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 C_f of 3.45 for Aethalometer harmonizes b_abs (Aethalometer) with b_abs (PSAP), b_abs (CLAP), and b_abs (MAAP) at Arctic sites.

Table 4 MAC_cor (Aethalometer; λ) and r² values at Alert during 2018–2019.

3.2 Ny-Ålesund

3.2.1 COSMOS–PSAP comparison

Simultaneous measurements of M_BC (COSMOS) for PM₁ and b_abs (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 b_abs values (PSAP; λ= 550 nm) were well correlated (r²= 0.76–0.82) with M_BC (COSMOS), and the MAC_cor (PSAP) value for the whole period was 14.4–15.2 m² g⁻¹ (Fig. 6a and b). Year-to-year variations in MAC_cor (PSAP) are also shown in Fig. 7a and Table 6. The correlation between b_abs (PSAP) and M_BC (COSMOS) during April–December 2012 was weak for unknown reasons. Excluding this period, average MAC_cor (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 MAC_cor (PSAP) values during 2014–2015 (Fig. 7a and Table 6) is not clear, this may be partly because b_abs (PSAP) data from December 2014 to April 2015 (during an “Arctic haze” period) were not available (Fig. S4a and b in the Supplement).

Table 5 MAC_cor (PSAP) and MAC_cor (Aethalometer) values derived from 24 h averaged data at Alert during 2018–2019.

^∗ MAC_cor (Aethalometer) values measured at λ= 470, 590, and 660 nm were adjusted to those at λ= 450, 550, and 700 nm (wavelengths used for PSAP) by assuming an absorption Ångström exponent of 1.0.

Figure 6 Correlations of M_BC (COSMOS) and b_abs (PSAP; λ= 550 nm) from April 2012 to September 2016 at Ny-Ålesund for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (PSAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

The MAC_med values of the b_abs (PSAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios were 16.7 and 17.2 m² g⁻¹ for the 1 and 24 h data, respectively, when the M_BC threshold of 2 ng m⁻³ was applied in the analysis (Fig. 6c and d). The MAC_med values were higher by 16 % and 13 % than MAC_cor for 1 and 24 h data, respectively (Table 3). Therefore, conversion of b_abs (PSAP; λ= 550 nm) to M_BC using a constant MAC_cor may result in a slightly biased M_BC, especially for lower b_abs data. This is partly because the correlation of b_abs (PSAP) with M_BC (COSMOS) is not very high, and scatter of the data, especially those with lower M_BC values, contributes to large variations in the b_abs (PSAP) $/M_{\mathrm{BC}}$ (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 b_abs measurements by PSAP at Ny-Ålesund may be a contributing factor, considering the higher correlations of b_abs (Aethalometer) and b_abs (MAAP) at Ny-Ålesund with M_BC (COSMOS) (Sect. 3.2.2 and 3.2.3). Based on the interquartile ranges of the b_abs (PSAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios, V_MAC 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 M_BC, if the constant MAC_cor value is used.

Table 6 Year-to-year variability of MAC_cor (PSAP; λ = 550 nm) and r² at Ny-Ålesund.

^a Average and standard deviation for individual years. ^b Derived by regression slope for all data points.

Table 7 Year-to-year variability of MAC_cor (Aethalometer; λ= 590 nm) and r² at Ny-Ålesund.

^a Average and standard deviation for individual years. ^b Derived by regression slope for of all data points.

3.2.2 COSMOS–Aethalometer comparison

Measurements of b_abs (Aethalometer; λ= 590 nm) for PM₁₀ were compared with measurements of M_BC (COSMOS) for PM₁ during 2012–2019. The time series data of b_abs (Aethalometer) were highly correlated with those for M_BC (COSMOS) (Fig. S5a and b in the Supplement) (r²= 0.90 for both the 1 and 24 h data; Fig. 8a and b). The MAC_cor (Aethalometer) values were 10.2 and 10.1 m² g⁻¹ for the 1 and 24 h data, respectively. Year-to-year variations in MAC_cor (Aethalometer) are also shown in Fig. 7a and Table 7. The r² values were generally high for each year, and the average MAC_cor (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 MAC_cor (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 MAC_cor 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 MAC_cor (Aethalometer) values (10.2 and 10.1 m² g⁻¹ for the 1 and 24 h data, respectively) were systematically lower than the MAC_cor (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 b_abs, as discussed in Sects. 1 and 2.2.3.

Figure 7 (a) Time series of yearly MAC_cor (PSAP; λ = 550 nm), MAC_cor (Aethalometer; λ= 590 nm), MAC_cor (MAAP; λ= 637 nm), and M_BC (COSMOS) at Ny-Ålesund. (b) Time series of yearly MAC_cor (PSAP–CLAP; λ= 550 nm) and M_BC (COSMOS) at Barrow. (c) Time series of yearly MAC_cor (MAAP; λ= 639 nm) and M_BC (COSMOS) at Fukue. In each panel, yearly MAC_cor and M_BC (COSMOS) are calculated from 1 h data. The dashed lines show the averages of yearly MAC_cor for the entire time series.

Figure 8 Correlations of M_BC (COSMOS) and b_abs (Aethalometer; λ= 590 nm) from April 2012 to August 2019 at Ny-Ålesund for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (Aethalometer) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

The MAC_med values of the b_abs (Aethalometer) $/M_{\mathrm{BC}}$ (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 MAC_med values for the 1 h data agree with MAC_cor to within 10 %, there is a 22 % discrepancy for the 24 h data under the assumed threshold setting (2 ng m⁻³) of M_BC (COSMOS) (Table 3). Therefore, conversion of 24 h averaged b_abs (Aethalometer; λ= 590 nm) to M_BC using a constant MAC_cor may be somewhat biased, especially for lower b_abs values (Fig. S5c and d in the Supplement). At Ny-Ålesund, the V_MAC was about 25 % for b_abs (Aethalometer; λ= 590 nm). The abovementioned bias leads to an additional uncertainty of about 20 % for conversion of 24 h averaged low b_abs data to M_BC, if the constant MAC_cor value is assumed.

3.2.3 COSMOS–MAAP comparison

Measurements of b_abs (MAAP; λ= 637 nm) without any particle size cut were compared with measurements of M_BC (COSMOS) for PM₁ during 2017–2020. The time series of b_abs (MAAP) and M_BC (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 MAC_cor (MAAP) values were 10.6 and 10.9 m² g⁻¹ for the 1 and 24 h data, respectively. These MAC_cor 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 M_BC measurements to determine MAC_cor (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 MAC_cor (MAAP) values.

Figure 9 Correlations of M_BC (COSMOS) and b_abs (MAAP; λ= 637 nm) from January 2017 to December 2020 at Ny-Ålesund for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (MAAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

Year-to-year variations in MAC_cor (MAAP) are also shown in Fig. 7a and Table 8. The r² values were generally high for each year, and the average MAC_cor (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 MAC_med values of the b_abs (MAAP) $/M_{\mathrm{BC}}$ (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 MAC_cor and MAC_med was limited to 3 % (Table 3). As discussed for the PSAP and Aethalometer in the previous sections, the relative uncertainty becomes higher when the M_BC values tend to be low (Fig. S6c and d in the Supplement).

Table 8 Year-to-year variability of MAC_cor (MAAP; λ = 637 nm) and r² at Ny-Ålesund.

^a Average and standard deviation for individual years. ^b Derived by regression slope for of all data points.

The MAC_cor (MAAP) and MAC_cor (PSAP) at Ny-Ålesund are compared in Table 11 in Sect. 3.6 after adjusting measurement wavelengths. MAC_cor (PSAP) values are 17 % and 20 % larger than MAC_cor (MAAP) values for 1 and 24 h data, respectively. A custom-built PSAP was used at Ny-Ålesund. The systematic difference of b_abs 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.

3.3 Barrow

COSMOS and PSAP–CLAP comparison

Simultaneous measurements of PM₁ for M_BC (COSMOS) and b_abs (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 b_abs (PSAP) and b_abs (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 M_BC (COSMOS) data from June 2018 to May 2019 were unavailable due to problems with the COSMOS instrument.

The b_abs (PSAP–CLAP; λ= 550 nm) data were strongly correlated with those for M_BC (COSMOS) (r²= 0.88 and r²= 0.86; Fig. 10a and b), and the MAC_cor 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 MAC_cor (PSAP–CLAP) during 2012–2018 was stable at 11.0 ± 0.9 (1σ) m² g⁻¹ (Fig. 7b and Table 9). Yearly M_BC (COSMOS) values did not exhibit large changes during this period (Fig. 7b). The b_abs (CLAP) data were weakly correlated with M_BC (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 MAC_cor (PSAP–CLAP) by excluding the MAC value for 2019.

Table 9 Year-to-year variability of MAC_cor (PSAP–CLAP; λ= 550 nm) and r² at Barrow.

^a Average and standard deviation for individual years. ^b Derived by regression slope for all data points.

Figure 10 Correlations of M_BC (COSMOS) and b_abs (PSAP–CLAP; λ= 550 nm) from August 2012 to December 2019 at Barrow for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (PSAP–CLAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

The MAC_med values of the b_abs (PSAP–CLAP) $/M_{\mathrm{BC}}$ (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 MAC_cor values of 10.8 and 10.6 m² g⁻¹, respectively (Table 3). Therefore, when either MAC_cor or MAC_med is used for conversion of b_abs (PSAP–CLAP; λ= 550 nm) to M_BC, the resulting M_BC values differ by only about 4 %. The V_MAC was about 25 % for b_abs (PSAP–CLAP; λ = 550 nm) at Barrow (Table 3). Because of scatter in the data, especially at lower M_BC values (Fig. 10a and b), the interquartile ranges of the b_abs (PSAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios are much larger when M_BC (COSMOS) is less than 10 ng m⁻³ (Fig. S7c and d).

3.4 Pallas

COSMOS–MAAP comparison

Measurements of b_abs (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. M_BC (COSMOS) measurements began in July 2019; we used the data collected up to July 2020 in this study. The M_BC (COSMOS) data for about 3 months (February to April 2020) were unavailable due to an air sampling problem.

The b_abs (MAAP) 1 and 24 h values (Fig. S8 in the Supplement) were strongly correlated with those for M_BC (COSMOS) with r²= 0.93 and r²= 0.95, respectively (Fig. 11a and b). MAC_cor (MAAP) was 13.0 m² g⁻¹ for both the 1 and 24 h data. This MAC_cor 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.

Figure 11 Correlations of M_BC (COSMOS) and b_abs (MAAP; λ= 637 nm) from July 2019 to July 2020 at Pallas for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regressions forced through the origin. (c, d) Corresponding histograms of b_abs (MAAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios for all data and data with M_BC (COSMOS) >2 ng m⁻³.

The MAC_med values of the b_abs (MAAP) $/M_{\mathrm{BC}}$ (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 MAC_cor (13.0 m² g⁻¹ for both 1 and 24 h data, Table 3). Therefore, the difference between the estimated M_BC values is less than 5 % when these MAC_cor or MAC_med values are used for conversion of b_abs (MAAP) to M_BC. The V_MAC was about 25 % for b_abs (MAAP) at Pallas (Table 3). The MAC_med values for low M_BC data (M_BC (COSMOS) <10 ng m⁻³) are very close to those for all datasets (Fig. S8c and d in the Supplement).

3.5 Fukue Island

3.5.1 COSMOS–SP2 comparison

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 M_BC (SP2) derived by integrating the mass size distributions over the detectable diameter range (D_m= 70–850 nm), we also estimated M_BC (SP2) in the D_m= 30–1000 nm range by fitting a lognormal function to the data. As the two sets of M_BC (SP2) values deviated by less than 2 %, we used the former M_BC (SP2) for comparison with M_BC (COSMOS). The time series of hourly values of M_BC (COSMOS) were strongly correlated (r²= 0.97) with M_BC (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 M_BC (COSMOS) and M_BC (SP2). Miyakawa et al. (2017) also reported a strong correlation (r²= 0.92; regression slope 1.14) between M_BC (COSMOS) and M_BC (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 M_BC (COSMOS) and M_BC (SP2) at Fukue was also examined on a logarithmic scale in Fig. S1b in the Supplement. When M_BC (SP2) is lower than ∼ 70 ng m⁻³, M_BC (COSMOS) tended to be slightly higher than M_BC (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).

3.5.2 COSMOS–MAAP comparison

Kanaya et al. (2013, 2016, 2020) made simultaneous measurements of M_BC (COSMOS) and b_abs (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 PM_2.5 cyclone was used instead. b_abs (MAAP) was highly correlated (r²= 0.94) with M_BC (COSMOS), and the MAC_cor (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 b_abs (MAAP) with M_BC (COSMOS) was also strong for individual years, MAC_cor (MAAP) for each year was also derived (Fig. 7c and Table 10). M_BC (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 MAC_cor (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 M_BC (COSMOS). This MAC_cor 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.

Table 10 Year-to-year variability of MAC_cor (MAAP; λ = 639 nm) and r² at Fukue.

^a Average and standard deviation for individual years. ^b Derived by regression slope for all data points.

Because the amount of data with M_BC less than 2 ng m⁻³ was very small at Fukue, the MAC_med values and the interquartile ranges of the b_abs (MAAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios were obtained for all data without applying any M_BC threshold. The MAC_med was 11.4 m² g⁻¹ for both 1 and 24 h data (Fig. 13c and d), which agrees well (within 6 %) with the MAC_cor 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 MAC_cor or MAC_med for conversion of b_abs (MAAP) to M_BC affects the resulting M_BC values by less than 6 %. The V_MAC was about 15 %, which is lower than those at Arctic sites (Table 3) partly because the higher M_BC (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.

Figure 12 (a) Number and mass size distributions of BC averaged over the observation period at Fukue in April 2019. The dashed (solid) red line is the lognormal fit to the number (mass) size distribution. (b) Time series (1 h data) and (c) correlation of M_BC measured by COSMOS and SP2. The solid red line in the correlation plot is the least-squares regression forced through the origin.

Figure 13 Correlations of M_BC (COSMOS) and b_abs (MAAP; λ= 639 nm) from April 2009 to May 2019 at Fukue for (a) 1 h averaged and (b) 24 h averaged data. The solid red lines are the least-squares regression forced through the origin. (c, d) Corresponding histograms of b_abs (MAAP) $/M_{\mathrm{BC}}$ (COSMOS) ratios.

3.6 Spatial variability of MAC_cor and r²

In previous sections, we showed that the MAC_cor values depended on instrument and observation site. The values of MAC_cor (λ= 550 nm) and r² are summarized in Table 11. Here, the MAC_cor (MAAP; λ ∼ 637 nm) and MAC_cor (Aethalometer; λ = 590 nm) values were adjusted to those at λ= 550 nm by assuming an absorption Ångström exponent of 1.0 (i.e., a λ⁻¹ relationship). The unit-to-unit variations in b_abs measurements were reported to be within 5 % for MAAP (Müller et al., 2011), 6 % for PSAP (Bond et al.,1999), and 4 % for CLAP (Ogren et al., 2017), if the careful calibration of flows and filter sampling spot sizes of these instruments are made for individual units. Therefore, the spatial variations in MAC_cor values observed in this study likely reflect differences of aerosol properties at the observation sites.

Table 11 MAC_cor and r² for MAAP, PSAP–CLAP, and Aethalometer at λ= 550 nm at observation sites in this study.

^a Total suspended particles. ^b A PM_2.5 cyclone was used before November 2011. ^c MAC_cor (MAAP; λ ∼ 637 nm) and MAC_cor (Aethalometer; λ= 590 nm) values were adjusted to λ= 550 nm by assuming an absorption Ångström exponent of 1.0. ^d Average and standard deviation values were calculated excluding MAAP data at Fukue.

The values of MAC_cor (PSAP) at Alert and MAC_cor (PSAP–CLAP) at Barrow were both determined with a PM₁ size cut, and they differed by about 22 % for 1 h data. Differences in aerosol properties including mixing states of BC at these sites could contribute to the different MAC values, although this effect cannot be assessed quantitatively with only this dataset. The correlations of b_abs (PSAP) with M_BC (COSMOS) at Alert were somewhat higher (r²= 0.95–0.96) than those of b_abs (PSAP–CLAP) at Barrow (r²= 0.86–0.88). The stronger correlation of b_abs (PSAP) with M_BC (COSMOS) at Alert suggests that environmental conditions including LSP $/$ BC ratios and mixing states of BC were more stable at Alert. We found that, at Alert, b_abs (PSAP) data with loading and scattering corrections were strongly correlated with the uncorrected b_abs (PSAP) data, and the contribution of the loading and scattering corrections was about 35 %, on average. In contrast, at Barrow, the contribution of these corrections was about 63 %. This suggests that at Alert, the LSP $/$ BC ratio was small and stable, and the influence of LSPs on derived b_abs (PSAP) was small. The greater distance from continental sources of aerosols at Alert than at Barrow (Fig. 1) may contribute to these observed differences.

At Ny-Ålesund, where a PM₁₀ inlet was used, the MAC_cor (PSAP) values were higher than those at Alert and Barrow. Also, the r² values at Ny-Ålesund (r²= 0.76–0.82) were lower than those at Alert. Effects of particles larger than 1 µm including dust and sea salt may partly contribute to the larger MAC and lower r² values at Ny-Ålesund.

The MAC_cor (PSAP) and MAC_cor (Aethalometer) agree to within 4 % for 1 h data at Alert, in spite of the different particle size cut of the inlets. However, they differed by about 24 % for 1 h data at Ny-Ålesund. Although the agreements were somewhat better for 2015–2016 at Ny-Ålesund (Fig. 7a), the reason for the overall discrepancy is unknown. Furthermore, while the MAC_cor (PSAP) at Ny-Ålesund was higher than that at Alert, the opposite result was obtained by Aethalometers, which is not easily interpreted.

The values of MAC_cor (MAAP) determined at Ny-Ålesund and Pallas differ by about 18 %. This difference may be attributed to the difference of average mixing states of BC and properties of other co-existing aerosols, which were affected by environmental conditions. Because these are the only available MAC_cor (MAAP) datasets derived from M_BC (COSMOS) in the Arctic, it is difficult to further evaluate spatial variability.

We have shown that in general b_abs values obtained by PSAP, CLAP, Aethalometer, and MAAP were strongly correlated with M_BC (COSMOS) at all four Arctic sites, although the strength of the correlations differed somewhat among the sites. Based on the analysis of $b_{\mathrm{abs}}/M_{\mathrm{BC}}$ variations among these sites, MAC_cor and MAC_med were most stable for PSAP with a PM₁ inlet at Alert and most variable for PSAP with a PM₁₀ inlet at Ny-Ålesund (Table 3). The average MAC_cor (λ= 550 nm) values at these four Arctic sites were 13.0 ± 1.6 (1σ; 12 % of the average) and 13.1 ± 1.7 (1σ; 13 %) m² g⁻¹ for 1 and 24 h data, respectively (Table 11). However, these correlations and resulting MAC_cor values may not hold outside the Arctic, where environmental conditions can be very different, especially the mixing states of BC and amount of interference by LSPs.

Zanatta et al. (2016), using M_EC measured by the thermal–optical transmittance method with the EUSAAR-2 protocol instead of M_BC (COSMOS), reported the average MAC_cor value at λ= 637 nm for nine European background sites to be 10.0 m² g⁻¹. From this MAC_cor (λ= 637 nm) value, the value of MAC_cor at λ= 550 nm is calculated to be 11.6 m² g⁻¹ by assuming an absorption Ångström exponent of 1.0. Although their MAC_cor values were generally obtained using PM₁₀ inlets or without particle size cuts, their average MAC_cor value (= 11.6 m² g⁻¹) is about 11 % lower than our average MAC_cor value (13.0–13.1 m² g⁻¹) at four Arctic sites determined in this study. This discrepancy may be partly due to the different methods used to determine absolute mass concentrations of BC.

Mason et al. (2018) derived the values of MAC_cor (PSAP) and MAC_cor (CLAP) for PM₁ size range in biomass burning and agriculture fire plumes during the SEAC⁴RS aircraft observation campaign by using M_BC (SP2) data. They reported the MAC_cor (PSAP; λ= 532 nm) and MAC_cor (CLAP; λ= 532 nm) values to be 21.0 and 26.5 m² g⁻¹, respectively, which are about 60 % larger than the average MAC_cor value (13.0–13.1 m² g⁻¹) determined in this study. Although the causes for their very high MAC_cor values are not clear, one possible explanation given by Mason et al. (2018) is the considerable amount of additional absorbers other than BC, including tar balls, that might have existed in their samples. Also, strong lensing effects by BC coatings could contribute to the high MAC_cor values. Thus, the MAC_cor values can be highly dependent on environmental conditions, and those reported in the present study are considered to be site-specific values, although the variability (1σ) of our MAC_cor values at the four Arctic sites was within 13 % of the average MAC_cor value for these four sites.

4 Summary and conclusions

Long-term measurements of M_BC by ground-based instruments are needed to investigate changes in the emission, transport, and deposition of BC. Various types of filter-based absorption photometers, including the particle absorption soot photometer (PSAP), the continuous light absorption photometer (CLAP), the Aethalometer, and the multi-angle absorption photometer (MAAP), have been used in the Arctic. To date, the accuracy of M_BC estimated from absorption coefficients (b_abs) measured by these instruments has not been adequately assessed, mainly because of a lack of simultaneous and reliable M_BC measurements.

In this paper, we introduced a systematic methodology to derive M_BC from b_abs measured by these instruments. To obtain accurate values of M_BC, we used a filter-based absorption photometer with a heated inlet (COSMOS), which we calibrated to within 10 % uncertainty with an SP2 deployed in Tokyo. Individual COSMOS instruments used for field observations were calibrated against the standard COSMOS to within about 10 %. The accuracy of M_BC (COSMOS) has previously been demonstrated to be about 15 % by comparison with M_BC (SP2) for sites in Asia and the Arctic. The effect on M_BC (COSMOS) of interference by light-absorbing FeO_x particles was estimated to be only a few percent, owing partly to the particle size cutoff of 1 µm by the PM₁ cyclone used. This effect may be somewhat higher for the other filter-based absorption photometers equipped with larger particle size cuts. The two necessary conditions for application of our method are a high correlation of b_abs with independently measured M_BC and long-term stability of the slope of the regression, which represents MAC_cor.

We compared b_abs (PSAP–CLAP) with M_BC (COSMOS) at Alert (PM₁) for 2 years, Ny-Ålesund (PM₁₀) for 4 years, and Barrow (PM₁) for 7 years. The b_abs (PSAP–CLAP) was highly correlated with M_BC (COSMOS) at these sites. For 1 h data, the MAC_cor (PSAP–CLAP) at λ= 550 nm was 13.9 m² g⁻¹ at Alert, 14.4 m² g⁻¹ at Ny-Ålesund, and 10.8 m² g⁻¹ at Barrow. The V_MAC was 19 % at Alert, 37 % at Ny-Ålesund, and 22 % at Barrow (Table 3).

We also compared b_abs (Aethalometer) with M_BC (COSMOS) at Alert (total suspended particles) for 2 years and at Ny-Ålesund (PM₁₀) for 8 years. They were highly correlated, and the MAC_cor (Aethalometer; λ= 590 nm) for 1 h data was 12.5 m² g⁻¹ at Alert and 10.2 m² g⁻¹ at Ny-Ålesund. One of the manufacturer's suggested MAC (Aethalometer) values is given by 14 625 $/$ (λ × C₀), which corresponds to 7.1 m² g⁻¹ for λ= 590 nm and C₀= 3.5 and which is considerably lower than the values obtained in our study. The V_MAC was 22 % at Alert and 25 % at Ny-Ålesund (Table 3).

The b_abs (MAAP) and M_BC (COSMOS) were also compared at Ny-Ålesund (total suspended particles) for 4 years, at Pallas (PM₁₀) for about 1 year, and at Fukue (PM₁) for about 10 years. b_abs (MAAP) was highly correlated with M_BC (COSMOS) at these sites. For 1 h data, The MAC_cor (MAAP) at λ= 637 nm was 10.6 m² g⁻¹ at Ny-Ålesund and 13.0 m² g⁻¹ at Pallas. The MAC_med (MAAP) at λ= 639 nm at Fukue was stable at 11.1 ± 1.0 m² g⁻¹, despite a 50 % decrease in M_BC (COSMOS) during this period (Fig. 7c). The default setting of MAC (MAAP) by the manufacturer (6.6 m² g⁻¹) is about half the MAC_cor obtained in this study, indicating a similar overestimation of M_BC if the default value is used to convert b_abs (MAAP) to M_BC at these sites. For 1 h data, the V_MAC was 20 % at Ny-Ålesund, 27 % at Pallas, and 15 % at Fukue.

Our results show that Arctic M_BC can be derived from b_abs obtained from PSAP, CLAP, Aethalometer, and MAAP measurements with reasonable accuracy by using the MAC_cor obtained from the regression slope of the b_abs–M_BC correlation, especially for long data-averaging times. However, scatter in b_abs–M_BC (COSMOS) correlations indicate that the accuracy of this method will be somewhat lower than that achieved by direct measurement of M_BC (COSMOS). We also caution that the reliability of the use of b_abs data to derive M_BC at other locations, especially those outside the Arctic, is unknown. Rigorous comparisons with COSMOS or SP2 data, such as those of this study, are required if use of our method is to expand beyond the Arctic region. Moreover, long-term comparisons are desirable for accurate determination of the MAC_cor. Short-term comparisons will be of limited value for understanding the variability of MAC for each instrument and location.