Soot aerosol was sampled onto filters in an airborne phase and as a part of liquid solution. In the airborne aerosol tests, soot was blown into a cylindrical experimental chamber (0.8 m height × 0.45 m diameter) through a stainless-steel tube (25 mm outer diameter) consisting of a y-shaped bend of 130∘, creating a size separation of the aerosol. Essentially a virtual impactor, this setup allowed the smaller-sized particles to continue with the airflow into the chamber, while the larger (and heavier) particles were deposited into a waste pipe through inertial separation (see Sect. 2.2.3 for further description and results in Sect. 3.1.1). From the experimental chamber a sample inlet (copper, 6 mm outer diameter) simultaneously fed two PSAPs and a portable aerosol spectrometer (Grimm 1.108). One of the PSAPs had quartz-fiber-filter punches mounted, while the other had standard PSAP filters installed. This setup was alternated among the PSAPs in between the experimental runs during the experiment to have both PSAPs assessed with the different filters. In total, 22 different experimental rounds were made with various amounts of aerosol deposited to the substrates.

In the liquid experiments, the same soot batch and procedure were used as above, but the outlet pipe was submerged into a 20 L container filled with deionized, purified Milli-Q (MQ) water. From this liquid solution, different small amounts (between 10 and 100 mL) were extracted and mixed with additional MQ water to further dilute the sample (to a typical total volume of 400 mL). This was performed to get a range of filters with different EC concentrations and optical depths. The total number of liquid-generated filters was 35. Some selected liquid samples (n=10) were exposed to an ultrasonic bath (for at least 15 min) prior to filtration. All of the liquid solutions were filtered onto the same quartz filters used in the airborne test, applying the same filtering principles and analysis procedures as used previously (Svensson et al., 2018). Punches from dried filters had their transmittance first measured using a PSAP, followed by EC concentration measurements (TOM). This procedure was also applied to the quartz filters from the airborne experiment.

Absorption was measured with two Radiance Research three-wavelength PSAPs (S/N 90 and S/N 100) at λ=467, 530, and 660 nm (Virkkula et al., 2005). One of them was loaded with a Pallflex E70-2075W filter that is generally used with the instrument, while the other was loaded with micro-quartz-fiber filters (Munktell, grade T293). The flows were calibrated with a Gilian Gilibrator bubble flow meter and set to 0.5 L min-1. Higher flow rates were not used here, since the quartz filter tends to be more fragile and may not withstand higher flows. The sample spot diameters of the PSAPs were measured with an Eschenbach scale loupe with a 0.1 mm graduation 10 times each. The average diameters (± standard deviation) were 5.04±0.10 and 5.05±0.10 mm, giving corresponding spot areas of 19.9±1.6 and 20.0±1.6 mm2. The aim was to use identical face velocities, i.e., average velocity of aerosol perpendicular to the filter (e.g., Müller et al., 2014) through both filter materials. The essentially identical spot areas also meant that we had tuned the flow rates identically. In addition, to study whether the PSAPs themselves affect the results, we used both filter materials alternatingly, as mentioned above, resulting in half of the 22 quartz filter samples being collected on the PSAP S/N 100 and the other half on the PSAP S/N 90. Another custom-built one-wavelength PSAP (λ=526 nm; Krecl et al., 2007) used in Svensson et al. (2018) was also utilized in for transmittance analysis of all the filters after their production in the airborne and liquid experiments.

Punches (typically with an area of 0.64 cm2) taken from the quartz filters were determined for their OC and EC content with a Sunset Laboratory OCEC analyzer (Birch and Cary, 1996), using the EUSAAR 2 protocol (Cavalli et al., 2010). The analysis procedure is based on stepwise increases in temperature in a helium atmosphere for the first stage, during which OC is detected with a flame ionization detector. The second phase of the analysis consists of introducing oxygen into the temperature increases and the detection of EC. Pyrolysis of OC during the first phase is monitored by a continuous laser transmittance measurement. Once the transmittance has reached the initial value for the filter in the second phase, a separation split point between OC and EC is established.

During the airborne experiments a Grimm optical particle counter (OPC; 1.108) was used as a portable aerosol spectrometer for particle size distributions. The OPC was factory-calibrated with polystyrene latex (PSL) spheres that are white. Their scattering cross section is larger than that of BC particles, which leads to underestimation of particle diameter. We did not find published Grimm 1.108 calibrations with BC particles in the literature; thus we approximated the effect. By using the cross sections modeled by Rosenberg et al. (2012), we estimate that the diameters presented by the OPC are possibly lower by a factor of 2. In Fig. 2 we present both the original size distributions and those calculated by multiplying the diameters by 2.

The PSAP was calibrated with the standard filter material Pallflex E70-2075W by Bond et al. (1999; here referred to as B1999) and Virkkula et al. (2005). Ogren (2010; here O2010) presented an adjustment to the Bond et al. (1999) calibration, while Virkkula (2010; here V2010) updated the Virkkula et al. (2005) calibration. In all of these the absorption coefficient is calculated as 1σap=f(Trt)AQΔtln⁡Trt-ΔtTrt-sσsp, where f(Trt) is the loading correction function that depends on the transmittance Trt=It/I0, in which It is the light intensity transmitted through the filter at time t, I0 the light intensity transmitted through a clean filter at time t=0, A the spot area, Q the flow rate, and s the fraction of the scattering coefficient σsp that gets interpreted as absorption. This is usually called the apparent absorption and should be subtracted from the uncorrected absorption or treated as presented by Müller et al. (2014). If apparent absorption can be considered negligible, Eq. (1) becomes 2σap=f(Trt)AQΔtln⁡Trt-ΔtTrt. In the present work, this approach was adapted for two reasons: (1) σsp was not measured during the calibration experiment, and (2) the aerosol used in the experiment was very dark (soot from oil-based burning); thus the apparent absorption could be considered negligible.

The loading correction function f(Tr) can be further rewritten as f(Tr)=g(Tr)/Cref, where Cref is the multiple-scattering correction factor and g(Tr) at Tr = 1 is a loading correction function that equals 1 at Tr = 1 and increases when the filter gets darker, i.e., when Tr < 1: 3σap=1Crefg(Trt)AQΔtln⁡Trt-ΔtTrt. If there is only one time step t=Δt, and if before sampling, Tr = 1, then Trt-Δt = Trt=0=1, and 4σap=1Crefg(Trt)AVtln⁡1Trt=1Crefg(Trt)σ0, where Vt is the air volume drawn through the filter from the start of sampling at time t. The assumption of only one time step means that Eq. (4) presents the absorption coefficient from the start of sampling on the filter. According to the Bouguer–Lambert–Beer law, light intensity decreases exponentially as a function of the optical depth τ: 5It=I0e-τ⇔τ=ln⁡I0It=ln⁡1Trt. This is relevant especially in the present study, since the purpose is to improve estimation of absorption in filtered snow samples. In the analysis of a snow sample there is only one “time step”: I0 is the intensity of light transmitted through a clean filter, and It is the intensity of light transmitted through a filter through which the melted snow sample was filtered. Here the airborne data were also treated in a similar way: for each time step absorption was calculated from Eq. (4) from the start of sampling on the filter.

If we assume that the difference of the absorption coefficients of the PSAPs using the quartz and Pallflex filters, σap(Q) and σap(P), respectively, is due to the multiple-scattering correction factors of the two materials only, we can calculate 6Cref,Q=σap(Q)σap(P)Cref,P, where Cref,Q and Cref,P are the multiple-scattering correction factors of the quartz and Pallflex filters, respectively. However, this is an approximation only, since the difference of σap(Q) and σap(P) is also due to the different transmittances TrQ and TrP of the two filter materials at each time step and consequently different values of the loading correction. However, below we will use Eq. (6) for the estimation of Cref,Q.

The Cref,P values for Pallflex E70-2075W filter were calculated here from two published calibration experiments. The loading correction function of B1999 (with the O2010 adjustment) can be reformulated as 7f(Tr)=11.5557⋅Tr+1.0227. This can be further rewritten as 8f(Tr)=1Crefg(Tr)=12.578410.6034⋅Tr+0.3966, where Cref=2.5784. Similarly, the V2010 loading correction can be rewritten as 9f(Tr)=k0+k1(h0+h1ω0)ln⁡(Tr)=k01+k1k0(h0+h1ω0)ln⁡(Tr)=1Crefg(Tr)=1Cref1+k1k0(h0+h1ω0)ln⁡(Tr), where h0, h1, k0, and k1 are the constants presented in Table 1 in V2010 and the single-scattering albedo ωo=σsp/(σsp+σap). For the three wavelengths Eq. (10) becomes 10f467(Tr467)=12.6531-1.698(1.16-0.63⋅ω0)ln⁡(Trb),11f530(Tr530)=12.7931-1.788(1.17-0.71⋅ω0)ln⁡(Trg),12f660(Tr660)=12.8411-1.915(1.14-0.72⋅ω0)ln⁡(Trr), with Cref,467=2.653, Cref,530=2.793, and Cref,660=2.841.

When Cref has been determined, it is assumed that g(Tr) is the same for both filter materials.

If mEC is the mass of EC in the filter (corresponding to the spot area) through which the air volume of Vt flowed, the average mass concentration of EC in aerosol in the air volume is cEC,aerosol=mEC/Vt. If σap is the absorption coefficient calculated from Eq. (4), the MAC can be calculated from 13MAC=σapcEC,aerosol=1Crefg(Trt)AVtτmECVt=1Crefg(Trt)AτmEC=1Crefg(Trt)τmECA=f(Trt)τmEC/A. This applies for aerosol but also for the snow samples, since the analysis of EC mass in a filter yields the mass surface density mEC/A, where mEC is the mass of EC in the analyzed filter spot with the area A. In Svensson et al. (2018) we calculated apparent MAC values of EC in snow samples simply from MAC=τ/(mEC) without applying additional corrections for filter loading, which neither enhanced absorption by the filter medium nor light-scattering particles. Assuming that only loading and filter effects apply in the experiments presented here, the apparent MAC values presented were adjusted by using f(Tr,Q)=g(Tr)/Cref,Q.

The average size distribution measured with the Grimm 1.108 OPC shows that most particles larger than 1 µm (Fig. 2a) were efficiently removed from the air stream with the pre-separator (Fig. 1). This is uncertain, however, since the OPC was calibrated with white PSL spheres (as discussed in Sect. 2.2.3). Another important point is that the lower limit of the sizes the OPC measured was 300 nm and is probably even higher due to the above-mentioned calibration error. The particle number size distribution, nevertheless, suggests that there were large numbers of BC particles smaller than can be detected by the OPC, since the particle number concentration increases sharply with decreasing particle diameter (Fig. 2a).

The mass absorption and scattering coefficients, MAC and MSC, respectively, and single-scattering albedo ωo of single BC particles at λ=530 nm were modeled with the Mie code of Barber and Hill (1990) and the complex refractive index of 1.85–0.71i and a particle density of 1.7 g cm-3. Comparison of single-particle ωo size distribution (Fig. 2b) with the particle number size distribution (Fig. 2a) suggests that ωo varied in the range of ∼0.3–0.5. Modeling for the size distribution measured with the OPC yielded ωo≈0.51 and 0.54 when using the original OPC diameters and the diameters multiplied by 2, respectively. These ωo values can be considered to be upper estimates, considering that a large fraction of small particles were undetected. However, to take the ωo uncertainty into account, we calculated all V2010-related values by using four ωo values: 0.3, 0.4, 0.5, and 0.6.

The optical depths presented in Svensson et al. (2018) were measured with the custom-made PSAP of Stockholm University at λ=526 nm, which is slightly different than the commercial Radiance Research PSAP (λ = 530 nm). Therefore, before applying the corrections (determined in Sect. 3.1.3 below), we examined whether the transmittances measured with these two PSAPs agree. Transmittances of all Pallflex and quartz filters were measured with both instruments. The resulting scatter plot (Fig. 3) shows that the agreement is excellent between the PSAPs; thus we concluded that the corrections established in this paper could be applied to the results presented by Svensson et al. (2018).

Optical depths (τ) for both the Pallflex and quartz filters, τ(P) and τ(Q), respectively, were calculated from Eq. (5) at a 1 s time resolution. The τ(Q)-to-τ(P) ratios – here the τ ratio – had a wide range of values at 1 s time resolution, but most of them were >1:99.6 % of τ(Q)/τ(P)>1, and the average and median ratios were 1.21 and 1.16, respectively. To study how the τ ratio depends on filter loading, the data were classified into transmittance bins of a 0.025 width in the Tr(P) range of 0.3–1.0, and the averages and medians were calculated for each bin (shown in Fig. 4). The transmittance dependence on the τ ratio of individual samples was often controversial: in some samples it decreased from the beginning, and in some samples, it increased. We do not have an explanation of this, although the high concentrations in the mixing chamber – see the attenuation coefficients σ0 in Table 1 – are probably largely the factor behind this observation. However, for all data the average and median τ ratio depended on the filter transmittance so that for a fresh clean filter at Tr > 0.9, it was higher than for heavily loaded filters at Tr < 0.4 (Fig. 4). In addition to the 1 s data, the τ ratio at the end of each sampling period is plotted as a function of transmittance of the Pallflex filter in Fig. 4. For the end values of all samples there was no clear Tr dependence. The most important conclusion in Fig. 4 is that the τ ratio of the two filter materials depends on the filter transmittance. On average the ratio decreases with increasing loading even though the same amount of BC is collected on both filters. That suggests that the loading corrections to be applied depend on the filter material and that they do not differ just by a constant factor.

In sample runs 4, 5, 7, 16, 18, 19, and 20, the decrease in Tr was relatively slow, and we considered the bin averages and medians calculated from them to be the most suitable to be used for determining Cref. Sample 17 was also long, taking more than 6 min. Despite the similar settings used for filling the mixing chamber and the diluter, the τ ratio was completely different from the rest of the samples (Fig. 4). This outlier was therefore excluded from the analysis.

The two correction algorithms (B1999 and V2010) were next applied to both filter materials, and σap(Q) and σap(P) (at λ=530 nm) were calculated from Eq. (4) by using the Tr bin averages and median of σ0 and then the ratio of these two, σap(Q)/σap(P). When the constants within the correction methods, including the Cref, were the same for both filter materials, the ratio is close to 1.2 (Fig. 5). As mentioned previously, V2010 depends also on ωo, and due to the fact that we are unsure of the ωo of the aerosol, we present four lines (ωo=0.3, ωo=0.4, ωo=0.5, and ωo=0.6) in Fig. 4. The B1999 correction yields a slightly decreasing σap(Q)/σap(P), suggesting that only adjusting Cref would not be enough. The V2010 correction does not yield a clear Tr dependence on σap(Q)/σap(P), although it has high σap(Q)/σap(P) values in the Tr(P) range 0.6–0.85. They correspond to the local maxima of the average and median τ ratio shown in Fig. 4. Nevertheless, there are not enough data in this study to robustly test the correction algorithms. Therefore, all values are calculated with both of them. We next calculated the multiple-scattering correction factor Cref from Eq. (7) by using the Tr(P) bin averages of σap(Q)/σap(P). The averages and standard deviations over the Tr(P,530) range of 1–0.3 and for averaging of all four single scattering albedos, ωo=0.3, ωo=0.4, ωo=0.5, and ωo=0.6, are presented in Table 2. It is worth noting that Cref≈3.4 at λ=530 nm is close with published values for another commonly used absorption photometer, the aethalometer, that uses quartz filters backed with supporting cellulose fibers. For instance, values around 3.5 were reported by Segura et al. (2014), Zanatta et al. (2016), and Backman et al. (2017).