Multiple scattering correction factor of quartz filters and the effect of filtering particles mixed in water: implications to analyses of light-absorption in snow samples

Abstract. The deposition of light-absorbing aerosols (LAA) onto snow initiates processes that lead to increased snowmelt. Measurements of LAA, such as black carbon (BC) and mineral dust, have been observed globally to darken snow. Several measurement techniques of LAA in snow collects the particulates on filters for analysis. Here we investigate micro-quartz filters optical response to BC experiments where the particles initially are suspended in air or in a liquid. With particle soot absorption photometers (PSAP) we observed a 20 % scattering enhancement for quartz filters compared to the standard PSAP Pallflex filters. The multiple-scattering correction factor (Cref) of the quartz filters for airborne soot aerosol is estimated to ~3.4. In the next stage correction factors were determined for BC particles mixed in water and also for BC particles both mixed in water and further treated in an ultrasonic bath. Comparison of BC collected from airborne particles with BC mixed in water filters indicated approximately a factor of two higher mass absorption cross section for the liquid based filters, probably due to the BC particles penetrating deeper in the filter matrix. The ultrasonic bath increased absorption still further, roughly by a factor of 1.5 compared to only mixing in water. Application of the correction functions to earlier published field data from the Himalaya and Finnish Lapland yielded MAC values of ~7–10 m2 g−1 at λ= 550 nm which is in the range of published MAC of airborne BC aerosol.


1 Introduction 29 Soot consists of black carbon (BC) and organic carbon (OC) particles formed during the incomplete 30 combustion of carbonaceous fuels. As the most light-absorbing aerosol (LAA) by unit per mass, BC is 31 highly efficient in absorbing solar radiation, and is a vital component in Earth's radiative balance (Bond 32 et al., 2013). Once the particles are scavenged from the atmosphere, possibly far from their emission 33 source, BC can reach a snow surface and decrease the snow reflectivity (Warren and Wiscombe, 1980;34 Flanner et al., 2007). This will lead to accelerated and increased snowmelt, observed in different snow 35 aerosol. One instrument used for light absorption measurements is the Particle Soot Absorption 48 Photometer (PSAP), utilizing Pallflex filters. As an alternative for filter analysis of BC, another 49 approach is to apply the thermal-optical method (TOM), providing organic carbon (OC) and elemental 50 carbon (EC) mass. With this method, EC refers to the carbon content of carbonaceous matter (Petzold 51 et al., 2013). The technique involves a stepwise heating procedure, therefore creating a need to use 52 micro quartz fiber filters. These filters have been used in numerous studies with filtering snow and ice 53 samples, and thereafter analyzed to determine the EC and OC content of the samples (e.g. Hagler et al., 54 2007;Forsström et al., 2009;Meinander et al., 2013;Ruppel et al., 2014;Zhang et al., 2017). In 55 Svensson et al. (2018), measurements with TOM were combined with an additional transmittance 56 measurement to further characterize the LAA present on the filter samples. 57 58 The goal of this paper is to further investigate micro quartz fiber filters optical behavior when sampling 59 BC particles. This aim is pursued through laboratory studies of BC filter deposition in an airborne phase, 60 as well as when the same BC particles are mixed in water and filtered onto the quartz filters (to simulate 61 snow sampling). 62 63 2 Materials, instruments, and data analyses 64 2.1 Soot aerosol production and sampling 65 A schematic picture of the experiment is presented in Fig. 1, and the methods used in each step are 66 outlined below. Soot aerosol were sampled onto filters in an airborne phase and as a part of liquid 67 solution. In the airborne aerosol tests, soot was blown into a cylindrical experimental chamber (0.8 m 68 height × 0.45 m diameter) through a stainless steel tube (25 mm outer diameter) consisting of a y-shaped 69 bend of 130°, creating a size-separation of the aerosol. Essentially a virtual impactor, this set-up allowed 70 https://doi.org/10.5194/amt-2019-142 Preprint. Discussion started: 29 May 2019 c Author(s) 2019. CC BY 4.0 License. 124 During the airborne experiments a Grimm optical particle counter (OPC, 1.108) was used as a portable 125 aerosol spectrometer for particle size distributions. The OPC have been factory-calibrated with PSL 126 spheres that are white. Their scattering cross section is larger than that of BC particles which leads to 127 underestimation of particle diameter. We did not find published Grimm 1.108 calibrations with BC 128 particles in the literature, thus we approximated the effect. By using the cross sections modeled by 129 Rosenberg et al. (2012) we estimate that the diameters presented by the OPC are possibly lower by a 130 factor of 2. In Figure 2

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The PSAP has been calibrated with the standard filter material Pallflex E70-2075W by Bond et al. 136 (1999; here referred to as B1999) and Virkkula et al. (2005). Ogren (2010; here O2010) presented an 137 adjustment to the Bond et al. (1999) calibration, while Virkkula (2010; here V2010) updated the 138 Virkkula et al. (2005) calibration. In all of these the absorption coefficient is calculated as 139 the light intensity transmitted through the filter at time t, I0 the light intensity transmitted through a 142 clean filter at time t = 0, A the spot area, Q the flow rate, and s the fraction of the scattering coefficient 143 sp that gets interpreted as absorption and gets usually called the apparent absorption and should be 144 subtracted from the uncorrected absorption or be treated as presented by Müller et al. (2014). If apparent 145 absorption can be considered negligible, equation 1 becomes 146 In the present work, this approach was adapted for two reasons: 1) sp was not measured during the 148 calibration experiment and 2) the aerosol used in the experiment was very dark (soot from oil-based 149 burning), thus the apparent absorption could be considered negligible. 150

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The loading correction function f(Tr) can be further rewritten as f(Tr) = g(Tr)/Cref where Cref is the 152 multiple scattering correction factor and g(Tr) at Tr = 1 a loading correction function that equals one at 153 Tr = 1 and increases when the filter gets darker, i.e., when Tr < 1. 154 If there is only one time step t =t and before sampling Tr =1 then Trt-t = Trt=0 = 1 and 156 where Vt is the air volume drawn through the filter since the start of sampling at time t. The assumption 158 of only one time step means (4) presents the absorption coefficient since the start of sampling on the 159 filter. According to the Bouguer-Lambert-Beer law light intensity decreases exponentially as a function 160 of the optical depth  161 This is relevant especially in the present study since the purpose is to improve estimation of absorption 163 in filtered snow samples. In the analysis of a snow sample there is only one "time step": I0 is the intensity 164 of light transmitted through a clean filter and It the intensity of light transmitted through a filter through 165 which the melted snow sample has been filtered. Here the airborne data were also treated in a similar 166 way: for each time step absorption was calculated from (4) since the start of sampling on the filter. Comparison of the ap(quartz) (= ap(Q)) and ap(Pallflex) (=ap(P)) and keeping the published PSAP 170 calibration functions (B1999, O2010, and V2010) as standards for ap(P) we derive Cref for the quartz 171 filter by the following reasoning. If the same function g(Tr) is used for calculating both ap(Q) and 172 ap(P) and especially if the same Cref = Cref,P of the Pallflex filter is used for both filter materials the 173 ratio of the absorption coefficients at time t is 174 where h0, h1, k0, and k1 are the constants presented in Table 1 in V2010 and the single-scattering albedo 192 o = sp/(sp+ap). For the three wavelengths (10)

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If mEC is the mass of EC in the filter (corresponding to the spot area) through which the air volume of 201 Vt has flown the average mass concentration of EC in aerosol in the air volume is cEC,aerosol = mEC/Vt. If 202 ap is the absorption coefficient calculated from (4), the mass absorption coefficient (MAC) can be 203 calculated from 204 transmittances by the length of the sampling time, however, this was not always successful (as noted in 218 Table 1). Without dilution the aerosol concentration in the mixing chamber was very high with 219 attenuation coefficients 0 in the range of ~60000 -~90000 Mm -1 (see samples 1 and 2, Table 1). 220 Therefore we added a dilution valve (V1) and a HEPA filter (Fig. 1) after the first couple of experiment 221 runs, and had variations in the sample air to clean filtered air ratio, which lead to lower 0 in the range 222 of ~1000 -~30000 Mm -1 . The system was not always stable, resulting in different measured 223 concentrations for similar sampling times. The average size distribution measured with the Grimm 1.108 OPC shows that most particles larger 227 than 1 µm (Fig. 2a) were efficiently removed from the air stream with the pre-separator (Fig. 1). This 228 is uncertain, however, since the OPC has been calibrated with white PSL spheres (as discussed in 2.2.3). 229 Another important point is that the lower limit of the sizes the OPC measured was 300 nm, and is 230 probably even higher due to the above-mentioned calibration error. The particle number size 231 distribution, nevertheless, suggests that there were large numbers of BC particles smaller than the OPC 232 detects since the particle number concentration increases sharply with decreasing particle diameter (Fig.  233 2a). 234

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The mass absorption and scattering coefficients, MAC and MSC, respectively, and single-scattering 236 albedo o of single BC particles at  = 530 nm were modeled with the Mie code of Barber and Hill 237 (1990) and the complex refractive index of 1.85 -0.71i and a particle density of 1.7 g cm -3 . Comparison 238 of single-particle o size distribution ( Fig. 2b)  Optical depths () for both the Pallflex and quartz filters, (P) and (Q), respectively, were calculated 247 from (5) at a 1-second time resolution. The (Q)-to-(P) ratioshere the  ratiogot a wide range of 248 values at 1-second time resolution but most of them were > 1: 99.6 % of (Q)/(P) > 1 and the average 249 and median ratios were 1.21 and 1.16, respectively. To study how the  ratio depends on filter loading 250 the data were classified into transmittance bins of a 0.025 width in the Tr(P) range of 0.3 -1.0 and the 251 averages and medians were calculated for each bin (shown in Fig. 3). The transmittance dependence of 252 the  ratio of individual samples was often controversial: in some samples it decreased from the 253 beginning, in some samples it increased. We do not have an explanation of this although the high 254 concentrations in the mixing chambersee the attenuation coefficients 0 in Table 1are probably  255 largely the factor behind this observation. However, for all data the average and median  ratio depended 256 on the filter transmittance, so that for a fresh clean filter at Tr > 0.9, it was higher than for heavily-257 loaded filters at Tr < 0.4 (Fig. 3). In addition to the 1-second data the  ratio at the end of each sampling 258 period are plotted as a function of transmittance of the Pallflex filter in Fig. 3 In sample runs 4,5,7,16,18,19, and 20 the decrease of Tr was relatively slow and we considered the 262 bin averages and medians calculated from them to be the most suitable to be used for determining Cref. 263 Sample 17 was also long, taking more than six minutes. Despite the similar settings used for filling the 264 mixing chamber and the diluter, the  ratio was completely different from the rest of the samples (Fig.  265 3). This outlier was therefore excluded from the analysis. 266

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The two correction algorithms (B1999 and V2010) were next applied to both filter materials and ap(Q) 268 and ap(P) (at  = 530 nm) were calculated from (4) by using the Tr bin averages and median of 0 and 269 then the ratio of these two, ap(Q)/ap(P). When the constants within the correction methods, including 270 the Cref, were the same for both filter materials the ratio is close to 1.2 (Fig. 4). As mentioned previously, 271 V2010 depends also on o, and due to the fact that we are unsure of the o of the aerosol, we present 272 four lines (o = 0.3, o = 0.4, o = 0.5, and o = 0.6) in Fig. 4

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The slopes of the optical depths (f) vs. EC concentrations, when applying the transmittance-dependent 288 loading correction f(Tr,Q,V2010, o = 0.4), were different, and depended on how the soot aerosol were 289 deposited onto the filter ( Fig. 6a and b). For the airborne aerosol, the slope is 6.4 ± 0.2 m 2 g -1 ; while the 290 particles mixed in water (without the ultrasonic treatment) have a slope that is doubled (12.6 ± 0.5 m 2 291 g -1 ). Applying o = 0.5 and o = 0.6 loading corrections, the slopes of the airborne particles are 6.1 ± 292 0.2 m 2 g -1 and 5.7 ± 0.20 m 2 g -1 , respectively; while the slopes of the particles mixed in water (without 293 the ultrasonic treatment) are 12.0 ± 0.4 m 2 g -1 , and 11.3 ± 0.4 m 2 g -1 . The ratios for airborne to liquid 294 particles are 0.506 ± 0.026, 0.507 ± 0.026, and 0.508 ± 0.025 for the three choices of o in the 295 10 calculation. The difference in slope between the airborne and liquid particles is likely an effect of 296 penetration depth of the soot particles into the filter media, with the higher slope for liquid particles 297 reflecting a deeper penetration. Nevertheless, the ratio is named as the water-mixing factor fw  0.51 ± 298 0.03. In comparison, using f(Tr,B1999) for the airborne and the water-mixed particles the slopes for 299 optical depth f vs. EC concentration are 4.33 ± 0.13 m 2 g -1 and 8.31 ± 0.22 m 2 g -1 , respectively, 300 providing a ratio of fw  0.52 ± 0.02, essentially identical to that obtained from the V2010 correction. 301

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The slope of f vs. EC of the 24 analyzed samples treated in the ultrasonic bath was even higher (Fig.  303 6a and b), reflecting a probable greater penetration depth of the particles. When f(Tr,Q,V2010) is 304 calculated with o=0.4, o=0.5 and o=0.6, the slopes of f vs. EC of the particles mixed in water with 305 the ultrasonic treatment were 18.7 ± 0.8 m 2 g -1 , 17.8 ± 0.8 m 2 g -1 , and 16.9 ± 0.7 m 2 g -1 , respectively. 306 The average ± uncertainty of the ratios of the slopes of airborne and water-mixed particles with the 307 ultrasonic treatment is very stable, 0.34 ± 0.02. If we consider this value to be a product of a factor fs 308 representing the ultrasonic treatment and the above-presented factor fw we obtain the value fs  0.67 ± 309 0.04. When f(Tr,B1999) is used also for the water-mixed and ultrasonic-bath-treated particles the slope 310 of corrected optical depth f vs. EC concentration is 12.9 ± 0.4 m 2 g -1 , with the corresponding fs  0.65 311 ± 0.03. 312

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The factors are used for multiplying f(Tr,Q) = g(Tr)/Cref(Q), and so another way it can be interpreted is 314 that they affect the multiple scattering correction 315  Table 2. The uncertainties of CrefW(Q) and CrefSW(Q) were calculated with a standard error propagation 319 formula by using the standard deviations of Crefs in Table 2  The resulting scatter plot (Fig. 8) shows that the agreement is excellent between the PSAPs, thus we 343 concluded that the corrections established in this paper could be done to the results presented by 344 Svensson et al. (2018). 345

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We multiplied the  of the laboratory data of Svensson et al. (2018) with fSfWf(Tr,V2010,o=0.4,Q) 347 since an ultrasonic bath was used also in those experiments. The slopes of the chimney and NIST soot 348 decreased from ~40 m 2 g -1 and ~35 m 2 g -1 to 11.9 ± 0.9 m 2 g -1 and 9.6 ± 0.6 m 2 g -1 , respectively (Fig. 9a  349 and b). In the scatter plot of the chimney soot the two data points with the highest EC concentration of 350 ~0.04 g m -2 are possible outliers. When they are discarded from the regression the slope becomes 9.8 ± 351 0.5 m 2 g -1 , which is indicated by the red line in Fig. 9a. This is within the uncertainties and is essentially 352 the same as for the NIST soot. 353

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These values are now in the order of published MACs, but for chimney and NIST soot still considerably 355 larger than the 6.4 ± 0.2 m 2 g -1 obtained in the present work (section 3.2). The explanation to this 356 difference is not clear. However, the procedures of processing the chimney soot and the NIST soot were 357 not exactly identical to the one we used in the present work. Svensson et al. (2018)  For the re-evaluation of the field data presented by of Svensson et al. (2018) we multiplied the  with 366 fwf(Tr,V2010,o=0.4,Q) since the field snow samples were melted and then filtered through the quartz 367 filters. The slopes of the field samples from the Indian Himalaya and from Finnish Lapland decreased 368 from 17.1 ± 0.8 m 2 g -1 and 21.5 ± 0.8 m 2 g -1 to 7.5 ± 0.4 m 2 g -1 and 9.8 ± 0.5 m 2 g -1 , respectively (