The measurements took place at SMEAR II (Station for Measuring Ecosystem–Atmosphere Relations II; Hari and Kulmala, 2005). The measurement station is located in Hyytiälä, southern Finland (61∘51′ N, 24∘17′ E). SMEAR II is a rural measurement station, and it represents a boreal forest environment. The area around the station is mostly forests that consist mainly of Scots pine trees (Hari et al., 2013). The site is classified as rural, and there are no significant sources of pollution nearby. The area is sparsely populated; in the nearby area there are a few smaller towns and some scattered settlements. The closest bigger cities are Tampere (220 000 inhabitants) and Jyväskylä (140 000 inhabitants), and they are located 60 and 100 km away from the station.

The measurements of AOPs for PM10 particles were started in June 2006 with an integrating nephelometer (TSI model 3563) and an Aethalometer (Magee Scientific model AE31). Later on a particle soot absorption photometer (PSAP; Radiance Research 3λ model; Virkkula et al., 2005) and a multi-angle absorption photometer (MAAP; Thermo Scientific model 5012; Petzold and Schönlinner, 2004) were also used.

The measurement arrangement of the instruments that measured the AOPs is presented in Fig. 1. The schematic figure represents the measurement line from a period when all the instruments mentioned before were measuring in parallel, which was during 2014–2015. At the start of the measurement line, a pre-impactor removed all the particles that were larger than 10 µm in aerodynamic diameter (i.e., PM10 passed the pre-impactor). The airflow through another impactor, which removed all the particles larger than 1 µm (i.e., PM1 passed the impactor), was controlled by two valves. The valves changed the direction of the flow every 10 min, so in a 20 min measurement cycle the instruments were exposed for 10 min to the PM10 and then for 10 min to the PM1. To hinder the effect of changing inlets, the first few minutes of the measurements after the inlet switch were omitted. For the absorption instruments the first 3 min was omitted, and for the integrating nephelometer the first 5 min was omitted. The sample air was dried with Nafion dryers for the PSAP, AE31, and integrating nephelometer for the whole period and for the MAAP from March 2017. Also, a cavity attenuated phase shift (CAPS) extinction monitor (Aerodyne Research; Kebabian et al., 2007) is marked in Fig. 1 since it was part of the measurement line. However, due to technical issues CAPS data were not applied in this study.

Even though the measurements of AOPs have been conducted at SMEAR II since 2006, in this study, we consider only data measured after January 2012 until December 2017. This period was selected to have at least two absorption instruments running in parallel: the AE31 stopped operating in December 2017; the PSAP operated from January 2012 to March 2016, and the MAAP started operation in June 2013. Also, during this period there were only a few changes in the measurement line: in March 2017 the MAAP flow was decreased from 18 to 9 Lmin-1 and Nafion dryers were installed in front of the MAAP, and in November 2017 one of the two Nafion dryers was removed in front of the nephelometer.

The instruments measured AOPs at different wavelengths: the integrating nephelometer measured at three wavelengths (450, 550, and 700 nm); the AE31, the PSAP, and the MAAP measured at seven wavelengths (370, 470, 520, 590, 660, 880, and 950 nm), three wavelengths (467, 530, and 660 nm), and one wavelength (637 nm), respectively. Here, we report the typically used AE31 and PSAP wavelengths, which are reported in the AE31 manual and by Virkkula et al. (2005), respectively. These reported wavelengths deviate slightly from the ones measured and reported by Müller et al. (2011a) (see their Table 6). For the MAAP, we decided to use the wavelength reported by Müller et al. (2011a) since it more commonly used and it clearly deviated from the wavelength reported by the manual.

The data availability of all the instruments for the studied period sets is reported in Fig. S1 in the Supplement. Some of the data were missing or invalidated due to instrument malfunctions, too-high relative humidity (RH), or the absence of the instrument because of workshops or campaigns. If the RH exceeded 40 % in an instrument, the data were marked as invalid according to recommendations (WMO/GAW, 2016). Before the dryers were installed for the MAAP in March 2017, some of the MAAP data, especially from the summer, were invalidated due to too-high RH. During the cold season, the indoor temperature at the measurement cottage was higher than outdoors, and therefore the RH decreased when the sample air was warmed up to the indoor temperature (passive drying). However, in the summer the RH sometimes increased above the accepted limit since the passive drying was not enough due to minimal difference between the indoor and outdoor temperature.

As mentioned above, the σabs of aerosol particles at different wavelengths at SMEAR II was measured with three different instruments: an AE31, PSAP, and MAAP. Each of these instruments measured σabs by a filter-based technique, which means that the measurements were conducted for aerosol particles that were collected on a filter. The AE31 operated on a quartz fiber filter (Pallflex, type Q250F), the PSAP on a quartz fiber filter (Pall, type E70-2075W), and the MAAP on a glass fiber filter (Thermo Scientific, type GF10).

The AE31 and the PSAP have a similar measurement principle (Bond et al., 1999). Before σabs can be determined by using different correction algorithms, the instruments measure the attenuation coefficient (σATN), which is the attenuation of light through the sample collected on the filter. The equation for σATN is derived from the Beer–Lambert–Bouguer law: 1σATN=AQΔtln⁡It-ΔtIt=AQΔATNΔt, where A is the sample area on the filter, Q is the flow through the filter, and Δt is the length of the measurement period. It-Δt and It are the measured and normalized light intensities through the filter at the beginning of the measurement period (t-Δt) and at the end of the measurement period (t). The intensities are normalized by comparing them to the intensity measured through a clean reference spot. Normalizing the intensities accounts for possible drifts and changes in the intensities of the LEDs. ΔATN is the change in attenuation (ATN), which is calculated from the ratio of light intensity through a clean filter (I0) and through a loaded filter (It) as 2ATN=-ln⁡ItI0⋅100%. In addition to ATN, the filter loading can also be described by transmittance (Tr) 3Tr=ItI0-1, which can be also presented as a function of ATN (Tr=exp⁡(ATN/100%)). ATN and Tr represent essentially the same concept, but the way of expressing the change in intensity depends on the instrument used: ATN is traditionally associated with Aethalometer data and Tr with PSAP data.

In Eq. (1), A is typically a constant value defined by the manufacturer and Q is recorded and reported by the instrument. These values, however, might deviate notably from the real values, and therefore they should be measured and checked regularly. If these values differ from the reported ones, Eq. (1) needs corrections for A and Q. At SMEAR II, the sample flow of each instrument was regularly measured with a Gilian flow meter, and the Q reported by the instruments was corrected to match the Gilian measurements. For the PSAP and AE31 we used the A values of 18.1 and 54.8 mm2, which deviated from the default ones of 17.8 and 50.0 mm2, respectively. The A used by default in the MAAP matched the measured one, and therefore it was not corrected.

In a filter, the light is attenuated because of the absorption and scattering by the particles but also because of the scattering by the filter fibers, which is called multiple scattering. The scattering by the filter fibers increases the optical path of the light beam through the filter. Therefore, the probability of the light beam being absorbed by a particle increases. Because of the scattering in the filter medium, σATN is larger than σabs. Not only do the filter fibers scatter light, but also the embedded aerosol particles scatter light and cause so-called apparent absorption, which is typically considered by subtracting a fraction of scattering from σATN. In addition to the scattering by the fibers and particles, the increasing number of absorbing particles in the filter also affects the instrumental response. The signal response caused by the particulate absorption decreases with increasing filter loading. Absorbing particles induce a so-called shadowing or a loading effect, which decreases the change in the intensity (It-ΔtIt-1) as the filter becomes more loaded (Weingartner et al., 2003). This means that the instrumental response is nonlinear with increasing filter loading. The increasing filter loading has an opposite effect to the scattering of the filter fibers and particles: the absorbing particles collected on the filter decrease the optical path, and therefore the reported σATN for a loaded filter is lower than for a pristine filter. This nonlinearity is considered in the various correction algorithms presented in Sect. 2.3.1 and 2.3.2.

The measurement principle of the MAAP is different from that of the AE31 and PSAP (Petzold and Schönlinner, 2004). In addition to the light attenuation measurements, the MAAP also measures the backscattered light from the filter at two different angles. σabs is then obtained by using a radiative transfer scheme where the measurements of the backscattering and light attenuation are taken into account (Petzold and Schönlinner, 2004). Because of the backscattering measurements, the MAAP does not suffer as much from the filter artifacts as the Aethalometer and the PSAP. However, in very polluted environments the MAAP also suffers from a measurement artifact that has to be corrected (Hyvärinen et al., 2013), which at SMEAR II, however, is not the case.

At SMEAR II, the MAAP advanced the filter spot automatically once per day in 24 h intervals. The AE31 also advanced the spot automatically when ATN reached 120 at a 370 nm wavelength. The PSAP filters were changed manually, and the aim was to change the filter every second day, but due to weekends and holidays, the filters were sometimes changed only after several days. On average the PSAP filters were changed once every 3 d.

The reported uncertainties in the MAAP, PSAP, and Aethalometer are 12 %, 13 %, and as large as 50 %, respectively (Arnott et al., 2005; Ogren, 2010; Petzold and Schönlinner, 2004). Müller et al. (2011a) reported that the unit-to-unit variability in the PSAP, AE31, and MAAP was about 8 %, 20 %, and 3 %. It must be noted that the unit-to-unit variability is a lot smaller, about 2 %, for the new AE33 model (Cuesta-Mosquera et al., 2021). Since the uncertainty and unit-to-unit variability in the MAAP were a lot smaller than for the PSAP and AE31, we used the MAAP as the reference instrument for measuring σabs. However, even though the MAAP was used as the reference here, it must be remembered that like all the filter-based photometers, the MAAP also suffers from the cross sensitivity to purely scattering aerosols, and therefore it is not the best reference instrument (Müller et al., 2011a).

Each of the absorption photometers used in this study has its strengths and weaknesses that determine which instrument is the most useful in different situations. According to the uncertainty and unit-to-unit variability, the MAAP is the most precise instrument for monitoring σabs and black carbon (BC) concentration, which is typically derived from σabs measurements. Also, the backscattering measurements from the filter reduce the artifacts caused by the scattering aerosol particles and the filter-loading effect, making it a more accurate instrument. The MAAP changes the spot in a filter roll automatically, and therefore it does not require much assistance from the operator, and the instrument can run at a remote station as well. However, it measures σabs only at one wavelength, so it is not possible to perform the source apportionment or interpretation of the chemical composition of the absorbing particles, which requires measurements on several wavelengths (see Sect. 3.1 and Eq. 16). The AE31 has a very wide range of wavelengths, which makes the seven-wavelength Aethalometers, the AE31 and the new model AE33, widely used instruments. Like the MAAP, the AE31 also operates the filter roll automatically, so the instrument does not need that much assistance from the operator. Unfortunately, the problems with defining the errors caused by the filter material are not that well defined, and the instrument uncertainty and unit-to-unit variability in the AE31 are large. The uncertainty in and noise of the PSAP is smaller than those of the AE31, which makes the PSAP a popular instrument especially in areas with low concentrations. Even though the wavelength range is not as wide as with the AE31, the PSAP measures σabs at three wavelengths, allowing the use of applications that need the wavelength dependency of σabs. The PSAP filters have to be changed manually by the user, so the instrument is not the best option to deploy at a remote site, but then again the leakage through the filter tape is less than for the MAAP and AE31.

The σsca data are needed to subtract a fraction of particulate scattering from the σATN values in A2005, CC2010, B1999, and V2010. Measurements of σsca and σbsca are also needed in determining ω and the backscatter fraction (b; see Sect. 3.1 and Eq. 18), which are used to explain the observed variations in the results. ω is also used in CC2010.

σsca and σbsca were measured with an integrating nephelometer (TSI model 3565; Anderson et al., 1996). The integrating nephelometer measured σsca and σbsca at three wavelengths (450, 550, and 700 nm). Due to instrumental restrictions, the nephelometer can only measure σsca in the range of 7–170∘ and σbsca in the range of 90–170∘, and therefore a truncation correction is applied to σsca and σbsca measurements (Anderson and Ogren, 1998; Bond et al., 2009). The fractional uncertainty in the integrating nephelometer for PM10 has been reported to be ±9 % (Sherman et al., 2015). Since scattering by aerosol particles depends significantly on the particles' size, the particulate light scattering is sensitive to hygroscopic growth. To prevent this, the integrating nephelometer is operated with two Nafion dryers as shown in Fig. 1.

The intensive properties of aerosol particles are determined from the measurements of the extensive properties, which in our data are σabs, σsca, and σbsca. In addition to the chemical properties and size distribution, the extensive properties also depend on the number and volume concentration of particles. The intensive properties, however, are independent of the number of particles, and they depend only on the properties of the particles, such as the shape of the size distribution, chemical composition, and shape of the particles. Therefore, intensive properties are useful parameters as they indirectly indicate the properties of the particle population. The intensive properties used in this article are the Ångström exponent (α), single-scattering albedo (ω), and backscatter fraction (b), and they are presented below.

The Ångström exponent (α) describes the wavelength dependency of the optical properties, and it can be calculated for example for σabs and σsca to acquire the absorption Ångström exponent (αabs) and scattering Ångström exponent (αsca), respectively. α is defined by 16α=-ln⁡σ1σ2ln⁡λ1λ2, where σ1 and σ2 are the property for which α is calculated at wavelengths λ1 and λ2, respectively. α is typically used to interpolate or extrapolate optical properties to different wavelengths. This is useful for example in cases when instruments measure optical properties at different wavelengths and the measurements between different instruments need to be compared. The wavelength dependency also gives information about the size distribution, chemical composition, and sources of the particles: αsca depends on the size distribution of the particles, and αabs depends on both the chemical composition and the size distribution. αabs is typically used in a set of empirical equations that approximate the source of black carbon (BC) (Sandradewi et al., 2008; Zotter et al., 2017).

The single-scattering albedo (ω) describes how big the fraction of the total light extinction (σext=σabs+σsca) is due to scattering: 17ω=σscaσsca+σabs. The lower ω is, the darker the aerosol particles are, which is typically caused by a higher content of black carbon (BC); ω close to unity indicates that the particles are high in scattering material like sulfates or sea salt. Therefore, ω is a rough indicator of the chemical composition of the particles.

The backscatter fraction (b) describes the fraction of backscattering coefficient (σbsca; meaning that the light scatters in the backward hemisphere) of the total scattering coefficient (σsca): 18b=σbscaσsca. b is also size dependent. In the molecular size range it is 0.5, which means that the particles scatter light evenly in the forward and in the backward direction. For larger particles b decreases, so the particles scatter light more in the forward direction.

As stated by Weingartner et al. (2003), Cref should in principle only depend on the instrument and the filter material used. The effect caused by different numbers of particles deposited in the filter material and their optical properties should be taken into account by the empirical filter-loading correction functions R(ATN). However, as shown by previous studies, Cref varies both spatially and temporally (Backman et al., 2017; Collaud Coen et al., 2010), and therefore we also determined Cref at SMEAR II.

In this study, the multiple-scattering correction factor (Cref) was defined for the AE31 measurements by using the σabs measured by the MAAP as the reference absorption coefficient (σabs,ref). To determine Cref, the σATN measured by the AE31 had to be corrected for the artifact caused by the increased filter loading, and then the measurements could be compared to the reference absorption (σabs,ref) measured by the MAAP: 19Cref=σATNR(ATN)σabs,ref. Cref was defined separately for data corrected using W2003, A2005, V2007, and CC2010 to obtain CWEI, CARN, CVIR, and CCOL, respectively. Cref was also determined for data that were not corrected for the filter loading (CNC, where subscript NC stands for non-corrected). Because the MAAP measures σabs,ref only on the 637 nm wavelength, the closest AE31 and nephelometer data were first interpolated to the same wavelength. σATN, ATN, and σsca were interpolated to 637 nm by applying the Ångström exponent explained in Eq. (16). Also, the wavelength-dependent constants used in W2003 and A2005 were interpolated to 637 nm. The f used in W2003 at 637 nm was 1.12, and the as,ARN and τa,fx used in A2005 were 0.0681 and 0.2009, respectively, at 637 nm.

In A2005, cumulative optical properties of the particles collected on the filter were needed, and thus CARN was determined by iteration; CARN was iterated for each filter spot until the median σabs,ref and σabs,ARN agreed within a 1 % limit. Because of the iteration, there is one CARN value for each filter spot. For other correction algorithms, the Cref value was determined by two methods: (1) as the slope of a linear regression for the whole data set (linear fit for a loading-corrected σATN-vs.-σref plot; Eq. 19) and (2) by simply using Eq. (19) to acquire the Cref value for each measurement point separately. In A2005, CARN depends on the wavelength. In this study CARN was determined only at 637 nm. Since we followed a similar procedure to that presented by Arnott et al. (2005), a fraction of σsca was first subtracted from σATN before determining CARN, which is different to Eq. (19).

The different Cref values were determined by a linear fit by comparing loading-corrected AE31 data to the reference data from the MAAP. Since Cref is described only by the slope of the fit, the intercept on the y axis of the fit was forced to be zero. For the linear fit we used all the available parallel data from the AE31 and MAAP. The Cref values were 3.00, 3.14, 2.99, and 2.77 for data corrected by W2003, V2007, and CC2010 and for data that were not corrected, respectively. The results and their statistical variability are presented in Table 2. The relatively small standard error (SE) and the range of confidence intervals (CI) indicate that the differences between the Cref values were statistically significant. However, for example, the difference between CWEI and CCOL was small.

The smallest determined Cref value was CNC, which was expected. Since σATN decreases for a loaded filter and the filter-loading correction was not applied, CNC had to be smaller than for the corrected data. Since the values of CWEI and CCOL were almost the same, the result suggested that the loading corrections RWEI and RCOL had on average a similar effect on the data. The highest value was determined for CVIR, which suggests that on average, the value of RVIR was the lowest (i.e., the effect of filter-loading correction in V2007 was stronger).

Since CARN was determined in an iterative manner for each filter spot, CARN was calculated as the median of all the filter spots and the resulting value was 3.13, which is also shown in Table 2. This result is not directly comparable to the other Cref values that were derived as a linear fit. Also, unlike the other algorithms, A2005 assumed a wavelength-dependent CARN. Here, we were only able to determine Cref at one wavelength by comparing the interpolated AE31 data to the MAAP measurements at 637 nm. To acquire CARN at all seven wavelengths of the AE31, we used the power law function CARN(λ)=CARN,637nm(λ/637nm)0.181=3.13⋅(λ/637nm)0.181, where the exponent 0.181 was obtained from a power function fitting to Cref vs. λ in Table 1 of Arnott et al. (2005), similarly to Virkkula et al. (2011). CARN,637nm=3.13 is the value determined above at λ=637nm. The results of the wavelength-dependent CARN values are presented in Table 3.

According to Collaud Coen et al. (2010), who studied the Cref values of different algorithms for ambient measurements in different environments, the higher Cref values were typically measured in polluted areas. Observations in our study support this claim. For example, the authors determined a mean CWEI of 2.81, 2.81, 3.05, and 4.09 at Hohenpeißenberg, Jungfraujoch, Mace Head, and Cabauw, respectively. Segura et al. (2014) obtained a Cref value of 4.22 measured in Granada, Spain, at 637 nm for the correction algorithm by Schmid et al. (2006). Compared to their study the Cref values at SMEAR II were obviously lower than the mean Cref values at the Cabauw and Granada measurement stations. Cabauw station is located near populated and industrial areas, and the station in Granada is located close to a highway. At SMEAR II, the average Cref values were somewhat higher than in the clean mountain stations in Hohenpeißenberg and Jungfraujoch. The closest values were defined for the Mace Head station, which observes mostly marine air. The Cref values by Collaud Coen et al. (2010) and Segura et al. (2014) were determined similarly to in our study, by comparing AE31 measurements against those of the MAAP.

Backman et al. (2017) determined Cf (Backman et al., 2017, used the symbol Cf instead of Cref to mark that the comparison was not conducted with a reference instrument) values for ambient data at several Arctic sites. They also derived Cf optically by comparing Aethalometer measurements against those of a MAAP, PSAP, and CLAP (continuous light absorption photometer; Ogren et al., 2017) They ran the comparison for Aethalometer data that were not corrected for the filter-loading error. The median Cf values at 637 nm were 1.61, 3.12, 3.42, 4.01, and 4.22 measured at Summit, Barrow, Alert, Tiksi, and Pallas, respectively. Backman et al. (2017) did not find any clear explanation for the very low Cf at Summit. At the other sites, the Cf values were rather high compared to the CNC observed at SMEAR II (CNC=2.77), which is unexpected if we assume that Cref was lower in clean environments, such as the Arctic, compared to at sites closer to pollution sources.

In laboratory runs, Arnott et al. (2005) determined Cref=2.076 (at 521 nm) for kerosene soot by comparing an AE31 against a photoacoustic instrument, and Weingartner et al. (2003) observed Cref=2.14 (averaged over wavelengths) for non-coated soot particles by subtracting scattering from extinction measurements. Compared to the Cref determined in laboratory studies by Weingartner et al. (2003) and Arnott et al. (2005), the ambient measurements in our study yielded higher values. This was also observed by Arnott et al. (2005), who suggested Cref=3.688 (at 521 nm) for ambient measurements, which is closer to our observations. In addition to non-coated soot, Weingartner et al. (2003) determined Cref for coated particles as well, and the resulting Cref was higher, about 3.6. This is also closer to our observations, which is explained by the fact that at SMEAR II, the observed soot particles are likely aged and coated since there are no significant local emission sources. In these studies, however, the reference instruments were not filter-based photometers, and that can have an effect on the results.

Report 227 by WMO and GAW recommends determining σabs from Aethalometer measurements by using a Cref value of 3.5 and not applying any filter-loading correction or particle-scattering reduction to the data. Cref was determined as an average over several data sets collected from different GAW stations. Comparing this value to CNC, using the recommended Cref=3.5 would systematically underestimate σabs at SMEAR II by ∼20 %. It must also be noted that due to the lack of R(ATN) correction, the BC concentration or σabs may differ by as much as 50 % even if the true σabs were to stay constant (Arnott et al., 2005). Therefore, in some cases, the data user may want to take the error caused by the filter loading into account and to use different correction algorithms, for example, when studying shorter time periods (e.g., a few days of data, which may fit a few filter spot changes causing apparent variation in the measured concentration).

There are both studies where a constant Cref has been used and studies where a wavelength-dependent Cref has been used. Others have observed no significant dependency of Cref on the wavelength (Backman et al., 2017; Bernardoni et al., 2021; Collaud Coen et al., 2010; Weingartner et al., 2003; WMO/GAW, 2016), and other studies have observed the opposite and shown that Cref is wavelength dependent (Arnott et al., 2005; Kim et al., 2019; Schmid et al., 2006). These studies suggested that Cref increased with wavelength (i.e., filter fibers scattered more light at longer wavelengths). Interestingly, even though the wavelength dependency was not statistically significant, Weingartner et al. (2003) reported that the Cref obtained for internal mixtures of diesel soot and ammonium sulfate and coated Palas soot yielded Cref=3.9⋅(λ/660nm)0.18 and Cref=3.66⋅(λ/660nm)0.23, respectively, as can be calculated from their Table 3. The exponents are very close to the value of 0.18 obtained from the fittings to the Arnott et al. (2005) Table 1. Kim et al. (2019) found that Cref depended on wavelength even more strongly; a fitting to their Table 2 yielded Cref=4.48(λ/532nm)0.48. Because the results between the different studies vary, it is difficult to conclude whether Cref is wavelength dependent or not. To study the wavelength dependency of Cref, it would be ideal to use a photoacoustic method or σext-σsca method for the reference measurements, since they are independent from the filter artifacts.

A newer model of the Aethalometer, AE33, applies the so-called dual-spot correction, so the instrument operators do not need to apply the correction algorithms themselves. However, the value of Cref is also an open question for the AE33, but since its filter material is different from the one used in the AE31, the results of the present study are not applicable to it. The filter material in AE33 is Teflon-coated glass filter tape (Pallflex type T60A20), but the “old” filter tape (Q250F) has also been used with AE33, and the recommended Cref values to use with these filters are 1.57 and 2.14, respectively (Drinovec et al., 2015).

The different Cref values were not only determined as a linear fit that considered the whole time series. In addition to the results from linear fits, Table 2 presents the median, mean, and standard deviation of different Cref values that were determined separately for each data point according to Eq. (19). Determining Cref separately for each data point enabled studying the temporal variation in Cref; for example, the times series of the different Cref values are presented in Fig. S2 in the Supplement. The median and mean values differed somewhat from the slopes of the linear fits, which were about 10 % lower than the median values. Comparing the median and mean values shows no large difference, meaning that the Cref values were rather normally distributed. The variation in median Cref values between the different correction algorithms was small compared to the relatively large standard deviation (see Table 2).

Cref, determined separately for each data point, was not stable over time (see time series presented in Fig. S2 in the Supplement), and we observed seasonal variation for Cref, which is presented in Fig. 2 for CNC as an example. The seasonal variation was observed not only for CNC but also for CWEI and CCOL, presented in Fig. S3 in the Supplement. Figure 2 shows that CNC was clearly above the median during the summer and below the median in winter and early spring. CNC reached its maxima in July and its minima in February. For CVIR and CARN, the seasonal variation was much less pronounced (Fig. S3 in the Supplement).

Since CWEI and CCOL had similar seasonal variation, it is unlikely that the seasonal variation observed for CNC was caused by the lack of filter-loading correction. There was seasonal variation for CCOL as well, and for example, the seasonal variations between CWEI and CCOL were rather similar, even though we applied constant f values in W2003. The CC2010 algorithm considers the wavelength dependency of scattering and the ω of the accumulated particles. It is rather surprising that taking these parameters, which have seasonal variation at SMEAR II (Luoma et al., 2019; Virkkula et al., 2011), into account did not seem to reduce the seasonality of Cref.

The seasonal variations in CARN and CVIR were less obvious than in CWEI, CCOL, and CNC. The lower seasonal variation for CARN might be explained by the subtraction of the scattering fraction before the loading correction was applied and CARN was determined. The fact that CARN has fewer data points than the other Cref values might also explain part of the lower seasonality. For CVIR, the lack of seasonal variation was probably caused by the very strong seasonal variation in the compensation parameter (k; see Fig. 9a) as will be discussed below in Sect. 4.4. The V2007 algorithm does not assume any coefficients but depends only on the difference between the last and first measurements of the filter spots. Therefore, it seems to adjust to seasonal changes, whereas the other algorithms apply coefficients. According to our results, V2007 and A2005 accounted for the variations in the optical properties of the particles embedded in the filter well, and therefore the seasonal variations in CVIR and CARN were reduced.

As indicated by the seasonal variation, Cref was not a constant value, but it depended on the optical properties of the particles embedded in the filter. As stated before, Weingartner et al. (2003) and Arnott et al. (2005) observed different Cref values for different types of aerosols, so Cref was lower for “pure” soot (no coating) and higher for coated soot or ambient aerosol particles. This suggests that Cref increases with increasing ω. This supports our observations, since at SMEAR II, ω is the highest in summer and lowest in winter (Luoma et al., 2019; Virkkula et al., 2011). However, Collaud Coen et al. (2010) observed a decreasing trend for Cref with increasing ω when they compared the average conditions at several stations.

ω, however, is not the only optical property of aerosol particles that had a clear seasonal variation (Luoma et al., 2019; Virkkula et al., 2011). For example, the size-dependent b and αsca reached their maxima in summer and minima in winter, which indicated that in summer the fraction of smaller particles increased. Luoma et al. (2019) showed that the seasonal variation in b and αsca is explained especially by the differences in the accumulation mode (particles in the size range of 100 nm–1 µm) particle concentration and size distribution: in summer, the volume concentration peaks at around 250 nm and in winter at around 350 nm. The size distribution affects the penetration depth of the particles as smaller particles penetrate deeper in the filter (Moteki et al., 2010). Scattering particles that penetrate deeper in the filter increase the multiple scattering in the filter, and that could be one explanation for higher Cref values observed in summer.

The differences in the scattering properties of differently sized particles might also explain the observed seasonal variation in Cref. The correction algorithms only consider the amount of scattering and not the direction of scattering. Smaller particles scatter relatively more light in the backward direction, which increases the optical path of the light ray through the filter (i.e., Cref should increase). Therefore, this effect may cause the observed increase in the multiple-scattering correction factor Cref in summer. This could also explain why CVIR had no seasonal dependency; the compensation parameter seemed to also depend on b (see Sect. 4.4), and that would make V2007 the only algorithm that takes the direction of the particulate scattering into account. Note that V2007 does not take b into account directly, but it seems to influence the calculated compensation parameter (see Sect. 4.4).

However, only very weak correlation was found between CNC and ω (R=0.17; p value<0.05) and CNC and b (R=0.23; p value<0.05), so ω and b do not necessarily explain the observed seasonal variations in the Cref values. For CWEI and CCOL, the results were similar, but for CVIR, the R values were even lower and even insignificant for ω.

We observed slightly higher correlation (R=0.30; p value<0.05) between CNC and relative humidity (RH), which is presented in Fig. 3 (the correlation was similar for CWEI and CCOL but weaker, about 0.09, for CVIR). Therefore, one possible reason for the observed seasonal variation in the different Cref values could be caused by changes in the instrumental RH and the RH differences between the MAAP and AE31. The RH presented in Fig. 3 was measured in the MAAP, and it varied between 5 %–40 % since the periods when the filter of the MAAP was exposed for RH equal to or larger than 40 % were excluded from this study. Because the AE31 was equipped with Nafion dryers, the RH in the AE31 varied less and was in the range of 5 %–20 %. The RH can influence filter-based optical measurements by affecting the optical properties of the aerosol particles and the filter fibers as well as by affecting the penetration depth of particles in the filter medium. The effect of the rate of change in RH on Cref was also studied, but the rate of change in RH did not show any correlation with CNC.

Due to hygroscopic growth, the aerosol particles scatter more light in humid conditions compared to dry conditions. The enhanced scattering induced by higher RH could then increase the scattering and optical path in a particle-laden filter medium. However, at SMEAR II, increasing RH should have caused a decrease in CNC, since hygroscopic growth would have increased the particulate scattering especially in the reference instrument MAAP. Hygroscopic growth may also affect the penetration depth of the particles in the filter (Moteki et al., 2010). When particles penetrate deeper in the filter, the effect of the multiple scattering is higher, increasing the measured σATN. Because the RH in the MAAP was higher than in the AE31, the particles directed in the AE31 may have penetrated relatively deeper in the filter than the particles directed in the MAAP filter, in summer, larger difference in the RH between the instruments could have increased the measured Cref. However, hygroscopic growth should not be significant in RH conditions below 40 %, which is why the effects related to hygroscopic growth seem unlikely explanations.

Also, the optical properties of the filter may change if the filter is exposed to high-RH conditions. The aerosol particles may take up water even below supersaturation, and when the liquid particles collide on the filter the moisture is taken up by the filter. Kanaya et al. (2013) compared a MAAP against a continuous soot monitoring system (COSMOS; Miyzaki et al., 2008) and actually observed a slight dependency in the σabs measured by the MAAP, so at low RH (<40%) σabs increased with increasing RH, which is contrary to our results as we observed that the MAAP observed relatively lower σabs at higher RH. However, the authors also observed the opposite behavior at higher RH (>50%). They suggested that the RH affected the surface roughness of the filter, which is used in the radiative transfer scheme (Petzold and Schönlinner, 2004), and therefore could have affected Cref.

The results showed that even though we excluded the high-RH data, the instruments seemed to be sensitive to variations in RH even below the recommended 40 %. However, the reason for the sensitivity remains unclear and would require more research and measurements, and therefore further analysis is omitted from the scope of this article.

In this section, we included data from June 2013 to February 2016 to have all three absorption instruments running in parallel to prevent any differences caused by different periods.

Since the σabs derived from AE31 measurements used the Cref values determined here, the σabs measurements of the AE31 and MAAP were expected to agree well, which is shown in Fig. 4. The AE31 data in Fig. 4 were produced by applying the Cref values determined from the linear fits (Table 2, column “Fit”). The correlation coefficients and slopes of the linear fits presented in Fig. 4 were close to unity. The AE31 correction schemes underestimated σabs only slightly, and the slopes varied from 0.96 to 1.00. The AE31 data corrected with A2005 and CC2010 underestimated σabs the most (slopes of the linear fits were 0.97 and 0.96, respectively). The reduction in particulate scattering in CC2010 after applying the multiple-scattering correction (i.e., Cref) could explain the slight underestimation in CC2010-derived data. For the underestimation in A2005-derived data, the reason is probably the different way of determining CARN compared to other Cref values. The iterative manner of determining CARN separately for each filter spot and then taking the median from these values was not as successful as the linear-fit method, which was used for the other algorithms. However, the underestimation for A2005 and CC2010 are only minor.

Surprisingly, the non-corrected (NC) AE31 data (Fig. 4e) did not seem to have a significant difference in the correlation coefficient compared to, for example, the data corrected with W2003 or CC2010 (Fig. 4a and d, respectively). However, the relation between σabs,NC and σref depended more on ATN than it did for any filter-loading-corrected data, which is shown by the color coding (ATN) of the data points and in Table 3, which presents the slopes of the linear fits and R2 values for different ATN intervals. If only data from a highly loaded filter (ATN>60 at 660 nm) were taken into account, the slopes of the linear fits were 0.97, 1.06, 0.99, 0.95, and 0.93 for W2003, A2005, V2007, CC2010, and NC, respectively. The smallest decrease in the slope with increasing ATN determined for the loaded filter was observed for data that were corrected by V2007. Interestingly, the slopes for the loaded filter increased for data that were corrected by A2005. This different behavior is probably caused by the fact that the A2005 algorithm did not consider the loading through ATN but applied a cumulative σabs, which apparently at SMEAR II seemed to overestimate the loading and loading correction, thus leading to an increasing slope with ATN. The biggest decrease in the slope determined for a highly loaded filter was observed for the NC data, as expected.

According to the R2 values presented in Table 3, the precision of the AE31 decreased with increasing ATN. For example, for the data corrected with the A2005 algorithm, R2 decreased from 0.96 for a clean filter (ATN<20) to 0.90 for a loaded filter (ATN>60). However, the decrease in R2 was quite minor. Miyakawa et al. (2020) also observed rather high R2 values between an Aethalometer (model AE51) and a reference instrument (single-particle soot photometer and COSMOS) when ATN was below 70, but when ATN exceeded 70, R2 decreased more rapidly. Unlike for the AE31, the loading on the filter did not seem to affect the precision of the PSAP at all as the R2 values did not decrease with increasing loading.

As presented in Table 3, the linear fits for the AE31 and PSAP data against the reference did not have an intercept of zero. This could be caused by the scattering artifact and the fact that the correction algorithms failed to take the scattering artifact partly into account. The intercept is the smallest for the B1999-corrected PSAP data and the largest for AE31 data. A fraction of σsca is subtracted in the AE31 algorithms by A2005 and CC2010. However, the data corrected with these algorithms still have a higher intercept than or similar intercept to the non-corrected data and the data corrected by the W2003 and V2007 algorithms. Considering the intercept, the V2007-corrected data perform the best in the AE31-vs.-MAAP comparison, which is slightly surprising, since it does not take the scattering subtraction into account. For the V2010-corrected PSAP data, the intercept is negative, suggesting that the V2010 algorithm overestimates the apparent absorption by scattering particles.

The comparison between the MAAP and the PSAP is presented in Fig. 5a and b and in Table 3 for both the correction schemes B1999 and V2010, respectively. Figure 5b shows that V2010 overestimated σabs especially when the loading was high (Tr was low), and the linear regression was 1.25. B1999 also overestimated σabs slightly, but in general it performed better in comparison with the MAAP, and the slope was 1.07 (Fig. 5a). The linear fits in Fig. 5a and b include all the data, but Table 3 presents the slopes of the linear fits for data with different Tr limits. It is actually recommended to use PSAP data with Tr>0.7, and if only these data are taken into account, especially the data corrected with the V2010 algorithm, they perform much better and have a slope of 1.01, but the data derived with the B1999 algorithm also yield a smaller slope of 1.04.

If all the data were included in the comparison, as in Fig. 5a and b, the overestimation of σabs would suggest also deriving the Cref values for the PSAP data. Here, we did not derive the Cref values for the PSAP since they are not typically used in a similar way to deriving σabs from the AE31 measurements. In general, the multiple scattering does not cause such a big artifact in filter material typically used in the PSAP compared to in the thicker AE31 filters. However, if we considered only the data where Tr<0.7, the PSAP and MAAP agree well for both correction algorithms. This result then suggests that there is no need for deriving a new Cref for the PSAP. Svensson et al. (2019) studied the multiple scattering in quartz filters, and they derived the equations that can be used in determining the Cref value for the PSAP. Differently to AE31 correction algorithms, the Cref used in PSAP algorithms is included in the coefficients of Eqs. (13)–(15), and therefore determining Cref for the PSAP is not as straightforward.

The differences between these two correction algorithms are studied in more detail in Fig. 5c, which shows how the algorithms perform with different Tr and ω values. As discussed before, V2010 produces notably higher σabs values when the filter is highly loaded (Tr<0.5). However, the difference between the algorithms depends not only on Tr but also on ω, so at high ω and Tr, σabs,PSAP,VIR/σabs,PSAP,BON<1, and when ω decreases the σabs,PSAP,VIR/σabs,PSAP,BON ratio grows. The reason for this is that the V2010 algorithm is a function of ω.

The dependency of σabs on ATN and Tr is presented in the Supplement (Figs. S4 and S5). On average, the decrease in σabs, which was not corrected for the filter loading (σabs,NC and σabs,PSAP,ATN), with the increasing ATN and decreasing Tr was not clear. This effect is better seen in the results presented in Table 3. However, Fig. S5 in the Supplement shows that especially for the PSAP, the use of correction algorithms decreased the variation, which is a strong recommendation for using the correction algorithms. This is also seen in the AE31 data, but the effect was less notable (Fig. S4 in the Supplement).

Because it is impossible to separate the effect of different size cuts from a loaded filter, here the PM1 and PM10 measurements were combined and averaged together. In general, PM1 accounted for about 90 % of the PM10 σabs; for σsca the fraction of PM1 was about 75 % (Luoma et al., 2019). Because absorbing particles, which are considered to consist mostly of black carbon, are typically in the fine mode (diameter<1µm), σabs is not expected to deviate much between the different size cuts. However, the differing size cuts, which cause more deviation in σsca, could have affected the σabs measurements since the particulate scattering causes apparent absorption and affects the multiple scattering in the filter. For example, the coarse particles (diameter>1µm) do not penetrate as deep in the filter as the fine-mode particles, which could possibly influence the Cref values. In an ideal situation the PM1 and PM10 absorption would have been measured by separate instruments.

Our observations underline the need for filter-loading correction, especially if one studies shorter time periods. For longer time periods (e.g., trend analysis or studies of seasonal variation), the effect of ATN on the variation smooths out, but for shorter time periods (e.g., case studies), the changing ATN can have a notable effect on the results if no filter-loading correction is applied. However, when not correcting for the filter-loading effect, the precision of the instrument and σabs or the BC concentration on average are reduced, which is why applying a filter-loading correction on filter-based photometers is always recommended.

The effect of the correction algorithms on αabs was studied, and the average αabs values for different correction algorithms of the AE31 and PSAP are presented in Fig. 6. This figure includes only parallel data from both the AE31 and the PSAP in order to avoid any differences caused by different time periods. For a comparison, αabs was also determined for the “raw” PSAP data that were not corrected by any algorithms (i.e., σATN; see Eq. 1). To have comparable αabs values from the different instruments, Fig. 6 includes only overlapping AE31 and PSAP data from 2011–2015. Since the PSAP operates at three wavelengths (467, 530, and 660 nm), we determined the AE31-related αabs in Fig. 6 by using only the wavelengths 470, 520, 590, and 660 nm of the AE31. The rest of the AE31 wavelengths were omitted from this comparison to minimize the effect of different wavelength ranges have on αabs (for example, see Luoma et al., 2019; Table 1). αabs was determined as a linear fit over all the selected wavelengths according to Eq. (16). Since Luoma et al. (2019) did not observe a big difference between the PM1 and PM10 αabs, we included both measurements in this comparison.

According to Fig. 6, the median values of αabs varied notably between the different instruments and correction algorithms: the lowest median value of αabs was 0.91, and it was measured by the AE31 and corrected by CC2010; and the highest median value of αabs was 1.48, and it was measured by the PSAP and corrected by V2010. The difference between the highest and lowest median values of αabs was about 1.6-fold. The correction algorithms were applied to each wavelength separately, and therefore the correction algorithms affected the wavelength dependency of the derived σabs. The scattering and loading corrections are different for each wavelength because for example σsca, ω, ATN, and Tr, which are used in the algorithms, are wavelength dependent. For the AE31, we studied the same five correction algorithms as in Sect. 4.1. The lowest median αabs values were observed for the non-corrected data (αabs,AE,NC) and for data that were corrected with the CC2010 and W2003 algorithms (αabs,AE,COL and αabs,AE,WEI). The median αabs values for the data corrected with the A2005 and V2007 algorithms (αabs,AE,ARN and αabs,AE,VIR) were higher at 1.28 and 1.21, respectively.

A2005 was the only algorithm that assumed a wavelength-dependent Cref. Since CARN increased with wavelength (i.e., bigger correction due to multiple scattering at higher wavelengths), taking the wavelength dependency of Cref into account increases αabs,AE,ARN compared to other algorithms. The correction factor of the V2007 algorithm depended on the difference between the ATN of loaded and clean filter spots. Most of the time ATN increased faster at short wavelengths than at long wavelengths, so the difference between the ATN of the loaded and clean filter spots was higher than for longer wavelengths. Therefore, the filter-loading correction was bigger for shorter wavelengths, and after the correction the difference between the σabs values at different wavelengths increased, increasing αabs as well.

For the PSAP data, the αabs values were generally a little higher compared to the AE31-derived αabs. The lowest PSAP-derived median value for αabs,PSAP,NC was 1.00, which resulted from data that were not corrected by any algorithm. B1999 resulted in a median αabs,PSAP,BON value of 1.03, and V2010 produced the highest αabs,PSAP,VIR overall, which was 1.48. A similar order of the average αabs values from different algorithms was observed by Backman et al. (2014) at an urban station in Elandsfontein, South Africa. For a data set measured off the east coast of the United States on a research ship, Backman et al. (2014) also reported the highest αabs for V2010. These results are consistent with each other. The explanation is that in V2010 all constants are wavelength dependent, contrary to in B1999.

The differences between the correction algorithms could possible be decreased by adding or reducing the wavelength dependency of the constant values used. Since we did not have reference measurements at several wavelengths, it is impossible to say which one of the correction algorithms yielded the most truthful value for αabs. This could be determined with several MAAPs operating at different wavelengths by measuring the particles suspended in the air by the photoacoustic method (Kim et al., 2019), by a polar photometer (Bernardoni et al., 2021), or by a multi-wavelength absorption analyzer (MWAA; Massabò et al., 2013). According to the comparison between an AE31 and an MWAA by Saturno et al. (2017), the best agreement for αabs was achieved with uncorrected AE31 data, and the AE31 data corrected by CC2010 also agreed well with the reference measurements.

We also studied if the αabs values were affected as the filter became more loaded with particles. Figure 7 presents the αabs values derived from AE31 data corrected with different algorithms as a function of ATN, and Fig. 8 presents the αabs values derived from PSAP data as a function of Tr. The αabs derived from corrected PSAP data (Fig. 8a and b) did not seem to depend on loading at Tr>0.4, but for higher filter loadings αabs still increased with decreasing Tr with both B1999 and V2010 corrections. In comparison, for the non-corrected PSAP data (i.e., σATN), αabs decreased with increasing Tr (Fig. 8c). The αabs values derived from the AE31 data were also studied; αabs,AE,WEI, αabs,AE,ARN, αabs,AE,COL, and αabs,AE,NC clearly decreased with increasing ATN. If ATN increased from 5 to 70, the decreases in αabs,AE,WEI, αabs,AE,ARN, αabs,AE,COL, and αabs,AE,NC were rather linear and around -22 %, -23 %, -33 %, and -27 %, respectively.

The αabs,AE,VIR derived from data corrected with V2007 did not seem to depend on ATN if not taking into account very high filter loadings (ATN at 660 nm >70; on average the filter changed when ATN at 660 nm ≈90). In V2007, k was determined for each wavelength separately. k is often larger for the shorter wavelengths, which means that the nonlinearity caused by the increased filter loading is relatively stronger at the shorter wavelengths (Drinovec et al., 2017; Virkkula et al., 2007, 2015), which was also observed by this study (discussed in the next section). According to these results, the algorithms other than V2007 do not seem to account for the wavelength dependency of R(ATN) enough.

The variation in k at SMEAR II has already been studied by Virkkula et al. (2007), who used AE31 data from December 2004 to September 2006. During this period, the AE31 was operating without any cutoff and there were no scattering measurements available, and this period was not included in our study. Here, we repeated the analysis for a longer time series and included the σsca measurements, so we could also determine b and ω.

The average values of k are presented in Table 4. The mean values of k varied from 4.6×10-3 at 370 nm to 2.0×10-3 at 950 nm. The wavelength dependency of k is described by ak, which is the slope of a linear fit of k over different wavelengths (kλ= akλ+k0; see example in Fig. 9b). A negative ak means that on average the filter-loading correction was greater at shorter wavelengths. The light attenuation is stronger at shorter wavelengths due to higher absorption and scattering by the particles, and therefore the shorter wavelengths are prone to bigger error caused by the filter loading. At longer wavelengths, the standard deviation of k was higher, meaning that k was more sensitive to the particle properties at longer wavelengths. The same observation was noted by Virkkula et al. (2015) as well.

At SMEAR II, we observed that k and ak had a very strong seasonal variation, so k and ak were the lowest in summer, which was also noted by Virkkula et al. (2007). The seasonal variation was observed at all wavelengths, but the variation was more pronounced at longer wavelengths. The seasonally averaged k and ak are presented in Table 4, and an example of the seasonal variation in k at 880 nm is presented in Fig. 9a. Similar seasonal patterns for k were also observed by Virkkula et al. (2007), Wang et al. (2011), and Song et al. (2013). In summer, the mean k values at the longer wavelengths (660–950 nm) were negative, meaning that without the correction, the AE31 would actually overestimate σabs at longer wavelengths.

Previous studies (e.g., Virkkula et al., 2007; Wang et al., 2011; Song et al., 2013) have suggested that the seasonal variation in k could be due to variations in ω, with lower ω inducing higher k. This behavior is observed at SMEAR II as shown in Fig. 9a and d; ω peaks in summer as k has its minima, and the correlation coefficient between ω and k is -0.47. The variation in ω also explains the observed negative k values. Virkkula et al. (2007) stated that the negative values are associated with the response of the Aethalometer to scattering aerosols as the negative k values are observed when ω is high. The effect of ω was taken into account, for example in the AE31 correction algorithms suggested by Weingartner et al. (2003), Arnott et al. (2005), and Collaud Coen et al. (2010). Virkkula et al. (2015) presented a theoretical explanation of the ω dependency of k, which our analysis supports.

Also, the effect being caused by the sizes of the particles has been suggested. The sizes of the particles affect their scattering properties and also their penetration depth in the filter that again could affect k. The size distribution of the particle population is described by b, with higher b indicating smaller particles. Müller et al. (2014), for example, showed that the effect of the asymmetry parameter, which is a function of b (Andrews et al., 2006), had an effect on the PSAP data.

The dependency of k on both b and ω was investigated more closely by Virkkula et al. (2015) at SORPES, an urban station located in Nanjing, China. The study showed positive correlation between k and b and negative correlation between k and ω. At SMEAR II, we also observed negative correlation between k and ω (Fig. 9c). However, contrary to the results by Virkkula et al. (2015), we observed negative correlation between k and b (Fig. 9d). Virkkula et al. (2015) discussed difficulties of showing whether b or ω was the dominant property in determining k. At SMEAR II, ω varies in a wider range compared to the observations at SORPES, which could explain some of the observed differences. The mean and standard deviation of ω at SMEAR II were 0.87±0.07 (at 550 nm; Luoma et al., 2019) and at SORPES 0.93±0.03 (at 520 nm; Shen et al., 2018). However, a clear reason for the negative correlation between k and b at SMEAR II was not found.