A comparison of three optical absorption photometers at a boreal forest site – effects of different correction algorithms

We present a comparison between three absorption photometers that measured the absorption coefficient (σabs) of ambient aerosol particles in 2012 – 2017 at SMEAR II, a measurement station located in a boreal forest in southern Finland. The comparison included an Aethalometer (AE31), a Multi Angle Absorption Photometer (MAAP), and a Particle Soot Absorption 10 Photometer (PSAP). These optical instruments measured particles collected on a filter, which is a source for systematic errors, since in addition to the particles, also the filter fibers interact with the radiation. To overcome this problem, several algorithms have been suggested to correct the data measured by the AE31 and the PSAP. Our aim is to study how the different correction algorithms affected the derived optical properties. We applied different correction algorithms to the AE31 and PSAP data, and compared the results against the reference measurements conducted by the MAAP. The comparison between the MAAP and 15 AE31 resulted to a multiple scattering correction factor (Cref) used in the AE31 correction algorithms to compensate for the scattering by the filter fibers. The Cref varies between different environments, and our results are applicable for measurements conducted in a boreal environment. We observed a clear seasonal cycle of Cref, which was probably due to the variations in aerosol optical properties, such as the backscatter fraction and single-scattering albedo, and also due to the variations in the relative humidity (RH) even though the RH in the instruments were kept below 40%. The results show that the filter 20 measurement methods seem to be rather sensitive to the RH even if the RH is below the recommended value of 40%. The instruments correlated well (R ≈ 0.98) but the slopes of the regression lines varied between the instruments and correction algorithms: compared to MAAP, the AE31 underestimated the σabs (the slopes varied between 0.93–0.97) and the PSAP overestimated the σabs (the slopes varied between 1.07–1.24). The instruments and correction algorithms had a notable influence on the absorption Ångström exponent: the median absorption Ångström exponent varied between 0.93 – 1.54 for the 25 different algorithms and instruments. https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Atmospheric aerosol particles have a notable effect on the Earth's radiative balance. The particles affect the climate directly by scattering and absorbing the radiation from the sun, and indirectly through the aerosol-cloud interactions (Stocker et al., 2013). According to the IPCC report (Stocker et al., 2013), one of the greatest uncertainties in determining the global radiative forcing is related to atmospheric aerosol particles. Reasons for the large uncertainty are the complex nature of the aerosol-5 cloud interactions and also the large spatiotemporal variation of aerosol particles (Lohmann and Feichter, 2005). Since the number concentration, size distribution, chemical composition and the shape of the particles vary in both space and time, it is challenging to model and estimate the effect that the aerosol particles have on the climate in global scale (Stocker et al., 2013).
Generally, the direct effect of the particles on climate is cooling, since most of the particles scatter the light from the sun back 10 in to the space (Stocker et al., 2013). However, if particles that are dark in color (i.e., highly absorbing) are located above a light colored surface (i.e., highly scattering), the particles have a warming effect on the climate. The sign of the aerosol forcing efficiency depends on the darkness of the particles, which is described by single scattering albedo, and on the albedo of the ground below the aerosol layer (Haywood and Shine, 1995). To determine the direct effect of the aerosol particles, in addition to the information about the albedo of the surface, we need measurements of aerosol optical properties (AOPs) like scattering, 15 backscattering and absorption coefficient (σsca, σbsca and σabs). The σsca describes the ability of the particles to scatter the light in all directions, the σbsca describes the amount of scattering only in the backward direction and the σabs describes the ability of the particles to absorb light. All these variables are wavelength dependent, which is why the measurements are preferably conducted at multiple wavelengths 20 Measuring the σsca and σbsca of aerosol particles is rather straightforward and the measurements are typically conducted with an integrating nephelometer. The error sources and uncertainties of nephelometer measurements are well known (Anderson and Ogren, 1998;Müller et al., 2011b). However, for the σabs measurements there are still large uncertainties and the error sources are not as well defined as for the scattering measurements. The main difference between the σsca and σabs measurements is that the σsca measurement are conducted for particles suspended in air, whereas the σabs is typically measured by filter-based 25 techniques, where the aerosol particles are first collected on a filter before the measurements. The problem with filter-based measurements is that in addition to the particles, also the filter fibers interact with the radiation, which influences the measurements.
One of the issues with the optical filter measurements is the multiple scattering of light by the filter fibers. The scattering by 30 the filter fibers is taken into account by the so-called multiple scattering correction factor (Cref). Even though the Cref should only depend on the filter properties, previous studies have shown that the Cref depends also on the particulate matter suspended in the filter Collaud Coen et al., 2010;Weingartner et al., 2003). The Cref has been observed to vary from https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. station to station and therefore it has been studied in different types of environments. For example, Collaud Coen et al. (2010) studied the Cref at very clean mountain sites, in a maritime site, and in more urban areas; Schmid et al. (2006) did observations in Amazonia; Backman et al. (2017) studied the Cref in Arctic sites; and Kim et al. (2019) ran measurements in a maritime, high altitude, and Arctic sites. In our study, one of the aims is to provide a Cref value suitable for a boreal forest site and to study how the Cref varies between different correction algorithms. 5 Another issue with the optical filter measurements is related to the nonlinear response of the instruments as the filter is loaded with particles. When the filter is loaded with absorbing particles, the particles cast a so-called shadowing effect, which decreases the response of the instrument. Therefore, the instruments report a lower σabs for loaded filters compared to pristine filter measurements. Several studies have developed algorithms and determined coefficients to overcome this problem 10 observed with different instruments Bond et al., 1999;Collaud Coen et al., 2010;Li et al., 2020;Müller et al., 2014;Ogren, 2010;Schmid et al., 2006;Weingartner et al., 2003;Virkkula et al., 2005;Virkkula et al., 2007;Virkkula, 2010). The outcome of the different algorithms, however, varies and they may affect for example the wavelength dependency of the σabs. Another aim of this study is to present how the different correction algorithms of the σabs affect the measured optical properties of the particles. 15 The measurements presented in this study, were conducted in 2012 -2017 at the SMEAR II (Station for Measuring Ecosystem-Atmosphere Relations II; Hari and Kulmala, 2005), which is located in the middle of a boreal forest in southern Finland. During this period, the AOPs at SMEAR II have been measured by several instruments: an integrating nephelometer and three different absorption photometers (AE31, PSAP, and MAAP), which enabled determining the Cref and an extensive comparison 20 between the different instruments and correction algorithms. AOPs at SMEAR II have been extensively discussed by Virkkula et al. (2011) and Luoma et al. (2019), however, these studies focused on the temporal variation of the AOPs and they only discussed nephelometer and AE31 data. In this study, we focus on the technical side of the measurements and instrument comparison.

The field site
The measurements took place at the SMEAR II station (Station for Measuring Ecosystem-Atmosphere Relations; Hari and Kulmala, 2005). The measurement station locates in Hyytiälä, Southern Finland (61°51'N,24°17 E). SMEAR II is a rural measurement station and it represents boreal forest environment. The area around the station is mostly forests, which consists mainly of scots pine trees (Hari et al., 2013). The site is classified as rural and there are no remarkable sources of pollution 30 nearby. The area is sparsely populated; are 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. https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.

Instrument set-up
The measurements of AOPs for PM10 particles were started already on June 2006 with an integrating nephelometer (TSI model 3563) and an Aethalometer (Magee Scientific model AE31). Later on there has also been a Particle Soot Absorption Photometer (PSAP; Radiance Research model 3-λ; Virkkula et al., 2005), a Multi-Angle Absorption Photometer (MAAP; 5 Thermo model 5012; Petzold and Schönlinner, 2004) and a Cavity Attenuated Phase Shift extinction monitor (CAPS, Aerodyne Research; Kebabian et al., 2007) . The CAPS was deployed at the SMEAR II to measure the extinction coefficient (σext) of airborne particles. However, the CAPS data was invalidated from this study due to technical issues and therefore the instrument is not discussed in this article. Even though the AOP measurements have been conducted at SMEAR II already since 2006, in this study we consider only data measured after January 2012 until December 2017. This period was selected 10 to have all the three 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 few changes in the measurement line: in March 2017 the MAAP flow was decreased from 18 lpm to 9 lpm and Nafion dryers were installed in front of MAAP; and in November 2017 one of the two Nafion dryers were removed in front of the

20
The data availability of all the optical data for the studied period sets are reported in Fig. 1. Some of the data were missing or invalidated due to instrument malfunctions, too high relative humidity (RH), too loaded filter, or due to the absence of the instrument because of workshops or campaigns. If the RH exceeded 40% in an instrument, the data was marked as invalid.
Before the dryers were installed for the MAAP in March 2017, some of the MAAP data, especially from the summer, had to be invalidated due to too high humidity. During the cold season, the indoor temperature at the measurement cottage was higher 25 than outdoors and therefore the RH decreased when the sample air was warmed up to the indoor temperature (passive drying).
However, during the summer the RH sometimes increased above accepted limit since the passive drying was not enough due to minimal difference between the indoor and outdoor temperature.
The measurement arrangement of the instruments, which measured AOPs, is presented in Fig 2. The schematic figure  30 represents the measurement line from that time when all the instruments mentioned before were measuring in parallel, which was during 2014 -2015. In the beginning of the measurement line, a pre-impactor removed all the particles that were larger than 10 µm in aerodynamic diameter from the sample air (i.e., PM10 particles passed the pre-impactor). The air flow trough https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
another impactor, which removed all the particles larger than 1 µm (i.e., PM1 particles passed the impactor) was controlled by two valves. The valves changed the direction of the flow in every 10 minutes, so that in a 20 minutes measurement cycle the instruments measured 10 minutes of the PM10 particles and then 10 minutes of the PM1 particles. The sample air was dried with Nafion dryers for the PSAP, AE31 and integrating nephelometer for the whole period and for the MAAP since March 2017. 5

Absorption measurements
As mentioned above, the σabs of aerosol particles at different wavelengths at SMEAR II was measured with three different instruments: AE31, PSAP and MAAP. Each of these instruments measure the σabs by filter-based technique, which means that the measurements are conducted for aerosol particles that are collected on a filter. 10 The AE31 and the PSAP have a similar measurement principle (Bond et al., 1999). Before the σabs can be determined by using different correction algorithms, the instruments measure the attenuation coefficient (σATN), which describes the attenuation of light through the sample collected on the quartz fiber filter. The equation for the σATN is derived from the Beer-Lambert-Bouguer law 15 where A is the sample area on the filter, Q is the flow through the filter, and t is the time. −Δ and are the measured light intensities through the filter in the beginning of the measurement period ( − Δ ) and in the end of the measurement period (t) and 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 20 In addition to the ATN, the filter loading can also be described by transmittance (Tr) which can be also presented as a function of ATN (Tr = exp(ATN/100%)). The ATN and Tr represent essentially the same concept, but the way of expressing the change of intensity depends on the instrument used: the ATN is traditionally associated 25 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. A should be checked regularly and Q should be monitored continuously and calibrated regularly with a calibrated flow meter. If these values differ 30 from the reported ones, the Eq. 1 needs corrections for the A and the Q. https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
In the 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 increase the optical path of the light beam through the filter. Therefore, the probability for the light beam to be absorbed by a particle increases. Because of the scattering in the filter medium, the σATN is larger than the σabs. Not only the filter fibers scatter light, but also the embedded aerosol particles scatter light affecting the absorption measurements, causing the so-called apparent absorption, which is 5 typically taken into account by subtracting a fraction of scattering from the σATN. As the filter gets more loaded with particles, the response of the instrument gradually changes. Absorbing particles induce a so-called "shadowing effect", introduced by Weingartner et al. (2003), decreases the change in the intensity ( −Δ −1 ) as the filter gets more loaded. This means that the response of the instruments is not linear for different filter loadings. The increasing filter loading has an opposite effect than the scattering of the filter fibers and particles: the absorbing particles collected on the filter decrease the optical path and 10 therefore the reported σATN for a loaded filter is lower than for a pristine filter. This non-linearity is taken into account in the various correction algorithms presented in Sect. 2.3.1 and 2.3.2.
The measurement principle of the MAAP is different from 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 in two different angles. 15 The 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 artefacts as the Aethalometer and the PSAP and hence it does not need any correction algorithms. However, in very polluted environments also the MAAP suffers from a measurement artifact that has to be corrected (Hyvärinen et al., 2013), which at SMEAR II, however, is not the case. 20 The reported uncertainties of the MAAP, PSAP and Aethalometer are respectively 12, 13, and as large as 50 % Ogren, 2010;Petzold and Schönlinner, 2004). Müller et al. (2011a) reported that the unit-to-unit variability of the PSAP, Aethalometer and MAAP were about 8%, 20% and 3%. Since the uncertainty and unit-to-unit variability of the MAAP was a lot smaller than for the PSAP and Aethalometer and because the measurement principle of the MAAP is independent from the 25 PSAP and AE31, since it uses the radiative transfer scheme, we used the MAAP as the reference instrument for measuring σabs.
Each of the absorption instrument used in this study have their 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 accurate instrument for monitoring σabs and black carbon (BC) concentration, which is typically derived from σabs measurements. The 30 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 the σabs only at one wavelength so it is not possible to do the source apportionment or interpretation on the chemical composition of the absorbing particles, which requires https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. measurements on several wavelengths (see Sect. 3.1 and Eq. 16). The AE31 again has a very wide range of wavelengths, which makes the seven-wavelength Aethalometers, the AE31 and the new model AE33, functional and popular instruments. Like 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 is large. The uncertainty and noise of the PSAP is smaller than that of the 5 AE31, which makes the PSAP a popular especially in areas with low concentrations. Even though the wavelength range is not as good as with AE31, the PSAP measures the σabs at three wavelengths, allowing the use of applications that need the wavelength dependency of σabs. The problem with PSAP is that the filter has to be changed manually by the user so the instrument is not the best option to deploy at a remote site.

AE31 correction algorithms
To determine the σabs from AE31 measurements, the σATN needs to be corrected for the multiple scattering by the filter fibers and for the error caused by the filter loading, and in addition, the scattering of aerosol particles should also be taken into

15
The effect of the multiple scattering is corrected with a multiple scattering correction factor (Cref) and it is larger than unity. The R, which equals unity for unloaded filters is less than unity for loaded filters, depends on the filter loading, i.e., ATN defined in Eq.
(2). 20 In Eq. (4), the scattering by the aerosol particles is taken into account by subtracting a fraction (as) of the measured scattering (σsca). However, the algorithms by Weingartner et al. (2003) and Virkkula et al. (2007) ignore the particle scattering subtraction, which makes it possible to apply the corrections algorithms without any σsca measurements. In Weingartner's algorithm, however, σsca is taken into account without the subtraction, as will be shown below. For a comparison, in this study we also 25 present data, which was corrected only for the multiple scattering and not for the filter loading (i.e., the R = 1) or scattering by the particles. Below we present the different algorithms determined by Weingartner et al. (2003), Arnott et al. (2005), Virkkula et al. (2007), and Collaud Coen et al. (2010, which were selected to use in this study. Current recommendation by the WMO and GAW is to assume the R(ATN) unity for the AE31 and to use a Cref value of 3.5, 30 which was determined by a comparison study of different AE31 instruments (WMO/GAW, 2016). Therefore, we also studied https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
"not-corrected" AE31 data for which we did not apply any R(ATN) correction or particulate scattering reduction, but only the multiple scattering correction.

Weingartner et al. (2003)
derived an empirical correction algorithm based on laboratory measurements of mixed particles (soot, diesel exhaust, organic coating, ammonium sulfate). Hereon we refer to the algorithm as W2003 and with the subscript 5 WEI. The W2003 correction algorithm interpolates the measurements at higher ATN values, to a point where ATN was 10%.
When ATN is lower than 10%, the R is assumed unity. In W2003 the loading correction RWEI is Weingartner et al. (2003) stated that the R is ω-dependent and they found the following relation for the factor f = (1 − ) + 1. (6)  10 In Eq. 6, the f is unity (i.e., R is unity), when the ω is unity (i.e., the aerosol is purely scattering). Weingartner et al. (2003) determined that the a in Eq. 6 was 0.87 and 0.85 at 450 and 660 nm, respectively. According to these values, we interpolated the a for all the seven wavelengths by assuming a linear wavelength dependency. Also, the ω was interpolated to the seven  based on a well-defined theoretical basis. One big difference to the W2003 is that there is a factor for scattering subtraction. Arnott et al. (2005) determined the scattering subtraction fraction as,ARN from laboratory measurements using submicron ammonium sulfate particles and the values for different wavelengths are presented in Table 1, however, Arnott et al. (2005) noted that the values of as,ARN could be different if supermicron aerosol particles are present. The loading correction RARN was 30 defined as: https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
where the n indicates the n th measurement after a filter spot change. The correction takes in to account the cumulative σabs of the particles collected on the filter material. The τa,fx(λ) is the filter absorption optical depth for the filter fraction x that has particles embedded. The used τa,fx values are presented in Table 1 and they were calculated from a power law function τa,fx(λ) = τa,fx,521‧(λ/521 nm) -0.754 = 0.2338‧(λ/521 nm) -0.754 . The exponent -0.754 was obtained from a power function fitting to τa,fx vs.

Virkkula et al. (2007)
proposed a correction algorithm, which is hereon referred as V2007 and with the subscript VIR, that utilizes the so-called compensation parameter (k). The k is determined by comparing the last measurements of a loaded filter to the first measurements conducted with a pristine filter. The compensation parameter is determined for each filter spot (fs) 10 as follows: where the "first" refers to the mean of three first values in a pristine filter (i.e., fs + 1) and the "last" refers to the mean of three last values in a loaded filter (i.e., fs). The k is then applied in the loading correction RVIR This algorithm does not take into account the scattering correction so the as,VIR = 0.
Collaud Coen et al. (2010) applied this correction to data from several stations in Europe and found that it was highly nonstable and that it leads to large outliers. They correctly stated that the difficulty of applying this correction is due to the natural high variability of ATN as a function of time, which is for most of the time greater than the ATN decrease induced by filter changes.

20
We therefore calculated the running average compensation parameter for all seven wavelengths in order to minimize these problems. Then we applied this averaged compensation parameter to correct the non-corrected AE31 data. In other words, the AE31 data were not averaged at this stage, just the compensation parameter.
We determined the k as a 14-day running mean (±7 days around the changing time of the filter spot), since without the 25 averaging the k was very noisy (see time series for the non-averaged and averaged k in Fig. S3). Averaging the k was also recommended by Virkkula et al. (2007). On average, the 14-day-periods included about nine data points (i.e., the filter spot changed on average about once a day). Virkkula et al. (2015) used a similar approach for AE31 data from Nanjing, China, and calculated 24-hour running averages of the k including on the average six filter spot changes.

30
Collaud Coen et al. (2010), which is hereon referred as CC2010 and with the subscript COL, correction algorithm was based on the W2003 algorithm but here the reference ATN for the clean filter is 0 % instead of 10 %. They determined the a used in https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
Eq. 6 a bit differently and got a mean value of a = 0.74 over different wavelengths and different experiments. The RCOL is defined as Here the ̅ 0, , stands for the mean ̅ 0, that was calculated for the filter spot from the first measurements to the n th measurement. The ̅ 0, , was determined by using the σATN as the first estimate of the σabs. CC2010 differs from the W2003 5 also by taking into account the scattering correction. They suggested two different kind of ways to determine as,COL and here we present the one that was determined in a manner similar to A2005. The difference to the as,ARN is that the as,COL is determined from the ambient scattering measurements so it is not constant. The as,COL is defined similarly as by Arnott et al. (2003) (Eq. 8 in their article), but here they used measured scattering properties instead of constant values determined by laboratory measurements: 10 where d = 0.564 and c = 0.329 ‧ 10 -3 . In Eq. 11 the over lined variables, αsca,n and βsca,n, stand for average properties of aerosols deposited in the filter i.e., mean values from the beginning of the filter measurements until the n th measurement. The αsca,n is the scattering Ångström exponent (see Sect. 3.1 and Eq. 16) and the βsca is acquired from the power-law fit of the wavelength dependency of σsca: 15 where the fit is calculated with λ and σsca in units nm and Mm -1 to acquire unitless β.

PSAP correction algorithms
Since the measurement principles of PSAP and AE31 are basically the same, the PSAP data needs similar kind of corrections as the AE31 data (Eq. 2). In this study the PSAP data was corrected with two algorithms: one described by Bond et al. (1999) 20 and later specified by Ogren (2010), which is hereon referred as the B1999; the other determined by Virkkula et al. (2005) and later corrected by Virkkula (2010), which is hereon referred as the V2010. The algorithms of Müller et al. (2014) and Li et al. (2020) were not applied.
in Virkkula (2010). The σabs,0 is used to calculate the single scattering albedo ω (see Sect. 3.1 and Eq. 17), which is then again used to calculate the σabs again in an iterative manner, but now with a different kind of an equation where the ℎ( 0 ) = ℎ 0 + ℎ 1 . The ω is then calculated again with Eq. 17. These two steps are repeated until the change in the σabs is minor. We agreed the result, when the change was less than 1%. It must be noted that this correction algorithm is 5 different from the V2007 determined for the Aethalometer data.

Scattering measurements
The σsca data is needed in order to subtract a fraction of particulate scattering from the σATN in A2005, CC2010, B1999 and V2010. Measurements of σsca and σbsca are also needed in determining the ω and the backscatter fraction (b, see Sect. 3.1 and 10 Eq. 18), which are used to explain the observed variations in the results. The ω is also used in CC2010.
The 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 on the range of 7° -170° and σbsca on the range of 90° -170°, and therefore a truncation 15 correction is applied to σsca and σbsca measurements (Anderson and Ogren, 1998;Bond et al., 2009). The uncertainty of the integrating nephelometer has been reported to be below ± 10 % (Anderson et al., 1996).

Data analysis
All the data were averaged for 1 h intervals. The PM1 and PM10 measurements were not separated in the data analysis, but instead both PM1 and PM10 data were averaged together. Since the instrument measured in the same size range, mixing the 20 PM1 and PM10 data cause no difference between the instruments.

Intensive properties
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 the particles. The intensive properties, however, are independent of the amount of the 25 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.
where the σ1 and σ2 are the property for which the α is being calculated at wavelengths λ1 and λ2, respectively. The α is typically 5 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 size distribution. The αabs is typically used in source apportionment models of black carbon (BC) (Sandradewi et al., 2008;10 Zotter et al., 2017).
One commonly used property is the single-scattering albedo (ω), which describes how big fraction of the total light extinction (σabs + σsca) is due to scattering: = sca sca + abs .
(17) 15 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 20 backward hemisphere) of the total scattering coefficient (σsca): The b is also size dependent. In 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 the b decreases, so the particles scatter light more in the forward direction.
Compared to αsca the b is less sensitive to bigger particles. 25

Multiple scattering correction factor
As stated by Weingartner et al. (2003), the Cref should in principle only depend on the instrument and the filter material used.
The effect caused by different amount 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, the Cref varies 30 https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
both spatially and temporally (Backman et al., 2017;Collaud Coen et al., 2010) and therefore we determined the Cref also 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 the Cref, the σATN measured by the AE31 had to be 5 corrected for the artefact caused by the increased filter loading and then the measurements can be compared to the reference absorption (σabs,ref) measured by the MAAP The Cref was defined separately for data corrected by W2003, A2005, V2007, and CC2010 to obtain the CWEI, CARN, CVIR, and CCOL respectively. The Cref was also determined for data, which were not corrected for the filter loading (CNC, where subscript 10 NC stands for "not corrected"). Because the MAAP measures the σabs,ref only on the wavelength 637 nm, the closest AE31 and nephelometer data were first interpolated to the same wavelength. The σATN and ATN measured by the AE31 and the 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 at 637 nm, respectively. 15 In the A2005, cumulative optical properties of the particles collected on the filter were needed, and thus the CARN was determined by iterating; the CARN was iterated for each filter spot until the median σabs,ref and σabs,ARN agreed within 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) a linear fit to σATN(R(ATN)) -1 vs. σabs,ref to acquire the Cref value for the whole data set; and by 20 2) simply using the Eq.19 to acquire the Cref value for each measurement point separately. In the A2005, the CARN depends on the wavelength. In this study the CARN was determined only at the 637 nm. Since we followed a similar procedure as presented by Arnott et al. (2005), a fraction of the σsca was first subtracted from the σATN, before determining the CARN, which is different to Eq. 19.

Multiple scattering correction for the AE31
The different Cref values were determined by a linear fit for loading corrected AE31 data vs. reference data from MAAP. Since the Cref is described only by the slope of the fit, the intercept in the y-axis of the fit was forced to be zero. For the linear fit we used all the available data. The Cref values were 3.00, 3.14, 2.99, and 2.77 for data corrected by W2003, V2007, CC2010, and for data that was not corrected, respectively. 30 https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
Since the CARN was determined in an iterative manner for each filter spot, the CARN was calculated as the median of all of the filter spots and the resulted value was 3.13, which is shown in Table 2. Unlike the other algorithms, the A2005 assumed a wavelength dependent CARN. Here, we were only able to determine the Cref at one wavelength by comparing the interpolated AE31 data to the MAAP measurements at 637 nm so we could not measure the CARN at different wavelengths. To acquire the CARN at all the seven wavelengths of the AE31, we used the power law function CARN(λ) = CARN,637nm(λ/637 nm) 0.181 = 3.13 ‧ 5 (λ/637 nm) 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), similar to Virkkula et al. (2011). CARN,637nm = 3.13 is the value determined above at λ = 637 nm. The results of the wavelength dependent CARN values are presented in Table 2.
The smallest determined Cref value was CNC, which was expected. Since the σATN decreases for a loaded filter and the filter 10 loading correction was not applied, the CNC has to be smaller than for the corrected data. The CNC was considerably lower than for example the CWEI and CCOL, which were about 8% higher than the CNC. Since the values of the CWEI and CCOL were almost the same, the result suggests that on average, the loading corrections RWEI and RCOL had similar effects on the data. The highest values were determined for CVIR and CARN, which were about 13% higher than CNC. The CARN was determined differently (iterative process for each filter spot) than other Cref values, which may partly explain the higher values. The CVIR, however 15 was determined similarly to CWEI and CCOL. The reason for the higher CVIR value is that on average, the value of the RVIR was lower than the RWEI or RCOL (i.e., the effect of filter loading correction in V2007 was stronger).
According to Collaud Coen et al. (2010), who studied the Cref of different algorithms for ambient measurements in different kinds of environments, the higher Cref values were typically measured in more polluted areas. Observations in our study support 20 this claim. For example, they determined mean CWEI of 2.81, 2.81, 3.05, and 4.09, at Hohenpeissenberg, Jungfraujoch, Mace Head, and Cabauw, respectively. Compared to their study the Cref values at the SMEAR II were obviously lower than the mean Cref values at the Cabauw measurement station, which is located near populated and industrial areas, and 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. In laboratory runs Arnott et al. (2005) determined Cref = 2.076 (at 521 nm) for kerosene soot and Weingartner et al. (2003) observed Cref = 2.14 (averaged over wavelengths) for not-coated soot particles. 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 not-coated soot, Weingartner et al (2003) determined the Cref for coated particles as 5 well and the resulted Cref was higher, about 3.6. This is also closer to our observations, which is probably explained by the fact that coated soot describes better the particles observed at SMEAR II, where the soot particles are likely aged and coated since there are no significant local emission sources.
The report 227 by WMO and GAW (World Meteorological Organization and Global Atmosphere Watch) recommends to 10 determine the σabs from Aethalometer measurements by using Cref value of 3.5 and not applying any filter loading correction or particle scattering reduction in the data. The Cref was determined as an average over several datasets collected from different GAW stations. Comparing this value to the CNC, using the recommended Cref = 3.5 would systematically underestimate the σabs at SMEAR II by about 20%. It must be also noted, that due to the lack of R(ATN) correction, the BC concentration or σabs may differ as much as 50% even if the real σabs would stay constant . Therefore, in some cases, the data 15 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., few days of data, which may fit few filter spot changes causing apparent variation in the measured concentration).
There are both studies where constant Cref has been used and studies where wavelength dependent Cref has been used. Others 20 observed no significant dependency for the Cref on the wavelength (Backman et al., 2017;Collaud Coen et al., 2010;Weingartner et al., 2003;WMO/GAW, 2016) and other studies observed the opposite and showed that the Cref is wavelength dependent Kim et al., 2019;Schmid et al., 2006). These studies suggested that Cref increases with wavelength (i.e. filter fibers scatter more light at longer wavelengths). It is worth pointing out that also Weingartner et al. (2003) presented slightly wavelength-dependent Cref values, even though in the literature mainly their average value of 2.14 is 25 cited. Interesting is also, that the wavelength dependency they obtained for internal mixtures of Diesel soot and ammonium sulfate and coated Palas soot yielded Cref = 3.9‧(/660 nm) 0.18 and Cref = 3.66‧(/660 nm) 0.23 , respectively, as can be calculated from their Table 3. The exponents are very close to the value 0.18 obtained from the fittings to the Arnott et al. (2005) Table   1. Kim et al. (2019) found during the Cheju ABC Plume Monsoon EXperiment (CAPMEX) that Cref depended on wavelength even more strongly, a fitting to their Table 2 yields Cref = 4.48(/532nm) 0.48 . In these three studies, the absorption standard was 30 a non-filterbased multiwavelength method.
The different Cref values were not only determined as a linear fit averaging over the whole time series. In addition to the results from linear fits, the Table 2 presents the median, mean, and standard deviation of different Cref values that were determined https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. separately for each data point according to Eq. 19. Determining the Cref separately for each data point enabled studying the temporal variation of Cref; for example the times series of the different Cref values are presented in Fig. S1. 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 of median Cref values between the different correction algorithms was small compared to the 5 relatively large standard deviation (see Table 2).
The Cref, determined separately for each data point, was not stable over time (see time series presented in Fig. S1) and we observed seasonal variation for the Cref, which is presented in Fig. 3 for the CNC. The seasonal variation was not observed only for the CNC, but also for the CWEI, CARN, and CCOL, which is presented in Fig. S2. The seasonal variation of the CVIR differed 10 from the other algorithms so that the seasonal variation was not as clear. Figure 3 shows that the CNC was clearly above the median during the summer and below the median in winter and early spring. The CNC reached its maxima in July and its minima in February.
Since the CWEI, CARN, and CCOL had a similar seasonal variation, it is unlikely that the seasonal variation observed for CNC was 15 caused by the lack of filter loading correction. It is actually rather surprising, that there was a seasonal variation for the CWEI, CARN, and CCOL as well. A2005 and CC2010 took into account the ambient ω, which has a clear seasonal variation at SMEAR II (Luoma et al., 2019;Virkkula et al., 2011), but against the assumptions, this is not seen in the results. For example, the seasonal variations between the CWEI and CCOL are surprisingly similar, even though we applied constant f values in W2003 However, the seasonal variation for CARN was a little less obvious than for CWEI, CCOL, and CNC, which might be because a 20 fraction of the σsca was subtracted before the loading correction was applied and the CARN was determined. The lack of seasonal variation for CVIR is probably caused by the very strong seasonal variation of the compensation parameter (k; see Fig. 10a) as will be discussed below. It seems that the V2007 is more dependent on the optical properties of the particles embedded in the filter than the other algorithms are and therefore the seasonal variation is reduced. The k is discussed more in Sect. 4.4.

25
The seasonal variations of the Cref values might be explained by the fact that the Cref is not necessarily a constant value, but it depends on the optical properties of the particles, which are embedded in the filter. As stated before, Weingartner et al. (2003) and Arnott et al. (2005) both observed different Cref values for different types of aerosols so that the Cref was lower for "pure" soot (no coating) and higher for coated soot or ambient aerosol particles. This would suggest that the Cref increases with increasing ω. This supports our observations, since at SMEAR II the ω is the highest in summer and lowest in winter (Luoma 30 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 several stations. https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
The 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 reach their maxima in summer and minima in winter, which indicates that in summer the particle size distribution had relatively more weight on smaller particles. Luoma et al. (2019) showed that the seasonal variation of b and αsca is explained especially by the differences in accumulation mode (particles in the size range of 100 nm -1 µm) particle concentration and size distribution: in summer, the volume concentration peaks 5 around 250 nm and in winter 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 of 10 Cref. The correction algorithms only take into account the amount of scattering, but not the direction of scattering. The smaller the particles are, the relatively more the particles scatter light in the backward direction increasing 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 the CVIR has no seasonal dependency; the compensation parameter seems to depend also on the b (see Sect. 4.4) and that would make the V2007 the only algorithm that takes the 15 direction of the particulate scattering into account. Note that the V2007 does not take the b into account directly but it seems to have an effect on the calculated compensation parameter.
However, only weak correlation was found between the CNC and ω (R = 0.17, p-value < 0.05), and CNC and b (R = 0.23, pvalue < 0.05), so there were only weak evidence on the dependency between the Cref and optical properties of the aerosols, 20 which could explain the seasonal variation of the Cref. However, we observed moderate correlation (R = 0. 30, p-value < 0.05) between the Cref and RH measured in the MAAP, which is presented in Fig. 4 for the CNC (the correlation was similar for CWEI, CARN, CVIR, and CCOL as well). Therefore, one possible reason for the observed seasonal variation of the different Cref values could be caused by a technical issue, which is related to the difference in the relative humidity (RH) between the instruments.
The RH presented in Fig. 4 was measured in the MAAP and it varied between 5 -40%; for the AE31, the RH varied less and 25 the RH was in the range of 5-20%. When the filter of the MAAP was exposed for RH equal or larger than 40%, the data was excluded from this study. Figure 4 shows that the CNC was higher when the sample air was more moist. 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 super saturation and when 30 the liquid particles collide on the filter the moisture is taken up by the filter. The RH may also affect the penetration depth of the particles in the filter, since the particles grow due to the water uptake (Moteki et al., 2010). When particles are penetrated 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 https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. particles directed in the MAAP filter. In winter, when the RH was low in both of the instruments the penetration depth would be more similar for each instrument. In summer, larger difference in the RH between the instruments could then increase the measured Cref. This result shows that even though we have excluded the high RH data, the instruments seem to be sensitive to variations in RH even below the recommended 40%. However, the penetration depth depends also on the filter material, which is different for MAAP and AE31. Further analysis is omitted here. 5

Performance of the correction algorithms
Since the σabs derived from AE31 measurements used the Cref values determined here, the σabs measurements of AE31 and MAAP were expected to agree well, which is shown in Fig. 5. The AE31 data in Fig. 5 was 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 10 in Fig. 5 were close to unity. However, all the AE31 correction schemes underestimateded the σabs a bit and the slopes varied from 0.93 to 0.97. The AE31 data corrected with the A2005 and CC2010 underestimated the σabs the most (slopes of the linear fits were 0.93). The reduction of particulate scattering in CC2010 after applying the multiple scattering correction (i.e., Cref) explains the underestimation in CC2010 derived data. For the underestimation in A2005 derived data, the reason is probably the different way of determining the CARN compared to other Cref values. The iterative manner of determining the CARN 15 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.
Surprisingly, the not corrected AE31 (Fig. 5e) did not seem to have a significant difference in correlation coefficient compared to for example to the data corrected with W2003 or CC2010 (Figs. 5a and d, respectively). However, the relation between the σabs,NC and σref seemed to depend more on the ATN than for any filter loading corrected data, which is shown by the color 20 coding (ATN) of the data points. If only data from highly loaded filter (ATN > 60) were taken into account, the slopes of the linear fits were 0.92, 1.00, 0.96, 0.90, and 0.88 for W2003, A2005, V2007, CC2010, and not corrected (NC), respectively. The smallest decrease in the slope determined for the loaded filter was observed for data that was corrected by V2007. Interestingly, the slopes for the loaded filter actually increased for data that was corrected by A2005, meaning that the RARN had a relatively big effect with increasing ATN. The biggest decrease in the slope determined for a highly loaded filter was observed for the 25 not corrected data, as expected. This observation underlines the need for filter loading correction if one studies shorter time periods. For longer time periods (e.g., trend analysis or studies of seasonal variation) the effect of the ATN 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.

30
The comparison between the MAAP and the PSAP is presented in Figs. 6a and b for both the correction schemes B1999 and V2010, respectively. The figure shows that V2010 overestimated the σabs when the Tr was low. For the whole data set the slope https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. of the linear regression was 1.24. If we calculate the linear regression for clean filter situations, when the Tr > 0.7 (at 660 nm), the slope of the linear fit is 1.01. For more loaded filter, with a limit of Tr > 0.5 (at 660 nm), the slope is 1.08.
The differences between these two correction algorithms are studied in more detail in Fig. 6c, which shows how the algorithms perform with different Tr and ω values. The figure shows that the V2010 produces notably higher σabs values when the filter 5 is highly loaded (Tr < 0.5). The difference between the algorithms depends also on the ω so that 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 is that the V2010 algorithm is a function of ω.

Absorption Ångström exponent for different correction algorithms 10
The effect of the correction algorithms on αabs were studied and the average αabs for different correction algorithms of the AE31 and PSAP are presented in Fig. 7. For a comparison, the αabs was also determined for the "raw" PSAP data that was not corrected by any algorithms (i.e., σATN, see Eq. 1). To have comparable αabs from the different instruments, Fig. 7 included 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. 7 by using only the wavelengths 470, 520, 590, and 660 nm of the AE31. The rest 15 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). The αabs was determined as -1×-slope of a linear fit to log(σabs) vs. log(λ) over the selected wavelengths. Since Luoma et al. (2019) did not observe a big difference between the PM1 and PM10 αabs, we included both measurements in this comparison. 20 According to Fig. 7, the median values of αabs varied notably between the different instruments and correction algorithms: the lowest median value of αabs was 0.85 and it was measured by AE31 and corrected by the CC2010; and the highest median value of αabs was 1.48 and it was measured by PSAP and corrected by the V2010. The difference between the highest and lowest median values of αabs was about 1.7-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 25 corrections are different for each wavelength because for example the 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 not corrected data (αabs,AE,NC) and for data that were corrected with the CC2010 and W2003 algorithms (αabs, AE,COL and 30 αabs, AE,WEI). The median αabs values for the data corrected with A2005 and 2007 algorithms (αabs, AE,ARN and αabs, AE,VIR) were higher, 1.20 and 1.19, respectively. Since we did not have reference measurements on several wavelengths, it is impossible to say which one of the correction algorithms yielded the most truthful value for the αabs. This could be done with several MAAPs https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. operating at different wavelengths or by measuring the particles suspended in the air by photoacoustic method (Kim et al., 2019).
The A2005 was the only algorithm that assumed a wavelength dependent Cref. Since the CARN increased with wavelength (i.e., bigger correction due to multiple scattering at higher wavelengths), taking the wavelength dependency of the Cref into account 5 increases the 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 at different wavelengths increased, increasing the αabs as well. 10 For the PSAP data, the αabs were generally a bit higher compared to the AE31 derived αabs. The lowest PSAP derived median value for αabs PSAP,NC was 1.01, which resulted from data that was not corrected by any algorithm. B1999 resulted for median αabs,PSAP,BON value of 1.04, and the V2010 produced the overall the highest αabs,PSAP,VIR, which was 1.48. Similar order of the average αabs from different algorithms was observed by Backman et al. (2014) at an urban station in Elandsfontein, South 15 Africa. For a dataset measured off the east coast of the United States on a research ship, Backman et al. (2014) reported also the highest αabs for the V2010. These results are consistent with each other. The explanation is that in V2010 all constants are wavelength dependent, contrary to the B1999.
We also studied if the αabs values were affected as the filter got more loaded with particles. Figure 8 presents the αabs derived 20 from AE31 data corrected with different algorithms as a function of ATN and Fig. 9 presents the αabs derived from PSAP data as a function of Tr. The αabs derived from corrected PSAP data ( Fig. 9a and b) did not seem to depend on loading at Tr > 0.4 but for higher filter loadings the αabs growed with decreasing Tr with both B1999 and V2010 corrections. As a comparison, for the not corrected PSAP data (i.e., σATN), the αabs decreased with increasing Tr (Fig. 9c). The αabs derived from the AE31 data was also studied; the αabs,AE,WEI, αabs,AE,ARN, αabs,AE,COL, and αabs,AE,NC clearly decreased with increasing ATN. If the ATN 25 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 the decreases were around -22, -23, -33, and -27%, respectively.
The αabs,AE,VIR, derived from data corrected with V2007, did not seem to depend on the ATN, if not taking into account very high filter loadings (ATN > 70). In V2007, the k was determined for each wavelength separately. In the next chapter, we show 30 that the k is typically largest for the shorter wavelengths, which means that the nonlinearity caused by the increased filter loading is relatively stronger at the shorter wavelengths. When this is not taken into account, the αabs decreases with the increasing ATN, which is seen with the other algorithms.

Variations of the compensation parameter
The variation of 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 cut-off 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 the b and ω. 5 The average values of the k are presented in Table 4. The mean values of the 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 the k over different wavelengths (k = ak + k0, see example in Fig. 10b). 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 10 and therefore the shorter wavelengths are prone to bigger error caused by the filter loading. At longer wavelengths, the standard deviation of the k was higher, meaning that the 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 the k and the ak had a very strong seasonal variation so that the k and ak were the lowest in 15 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 of k at 880 nm is presented in Fig. 10a. Similar seasonal pattern for the k were also observed by Virkkula et al. (2007), Wang et al. (2011), andSong et al. (2013). In summer, the mean k values at the longer wavelengths (660-950 nm) were actually negative, meaning that without the correction, the AE31 would actually overestimate the σabs at 20 longer wavelengths.
Previous studies (e.g., Virkkula et al., 2007;Wang et al., 2011;and Song et al., 2013) suggested that the seasonal variation in k could be due to variations in ω, so that lower ω induced higher k. This correlation is observed at SMEAR II as shown in Figs. 10a and d; the ω peaks in summer as the k has its minima and the correlation coefficient between the ω and k is -0.47. 25 The variation of 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 are observed when the 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. (2007), andCollaud Coen et al. (2010). Virkkula et al. (2015) presented a theoretical explanation to the  dependency of k, which our analysis supports. 30 Also, the effect caused by the sizes of the particles has been suggested. The particle sizes affect the scattering properties of the particles and also an effect on the penetration depth in the filter, which could affect the k. The size distribution of the particle https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License. population is described by the b so that higher b indicates smaller particles. Müller et al. (2014), for example, showed that the effect of 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. 5 At SMEAR II, we also observed negative correlation between k and ω (Fig. 10c). However, contrary to the results by Virkkula et al. (2015), we observed negative correlation between k and b (Fig. 10d). Virkkula et al. (2015) discussed about the difficulties to show whether the b or the ω was the dominant property in determining the k. At SMEAR II, the 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 10 et al., 2018). However, a clear reason for the negative correlation between the k and b at SMEAR II was not found.

Summary and conclusions
In this study, we presented a comparison of three different absorption photometers (AE31, PSAP, and MAAP), which measured ambient air at SMEAR II, a rural station located in middle of a boreal forest in southern Finland. We also compared different correction algorithms that are used in determining the absorption coefficient (σabs) from the raw absorption photometer 15 data. We studied how the algorithms affected the derived parameters and determined multiple scattering correction factor (Cref) applicable at SMEAR II.
To get more reliable AE31 measurements, the AE31 data were compared against the MAAP data to acquire the Cref that is used in the processing of the AE31 data. The resulted Cref values were 3.00, 3.13, 3.14, and 2.99 for the algorithms suggested 20 by Weingartner et al. (2003), Arnott et al. (2005), Virkkula et al. (2007), andCollaud Coen et al. (2010), respectively. Previous studies observed that the Cref varied between different types of environments and stations and here it was determined for the SMEAR II station, which represents the atmospheric conditions in a boreal forest. The Cref determined at the SMEAR II can be applied to other boreal forest sites as well. Even though the AE31 is the an old model and no longer in production, the results can be used in post-processing older data sets or at sites that still operate the older AE31. Newer model of the 25 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 an open question for the AE33 also 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.
We observed also a clear seasonal cycle associated with Cref, which was probably due to the variations in the optical properties 30 of the aerosol particles, such as the b and ω. We also observed some correlation between the Cref and RH even though the RH https://doi.org/10.5194/amt-2020-325 Preprint. Discussion started: 8 September 2020 c Author(s) 2020. CC BY 4.0 License.
in the instruments were kept below 40%. These results show that the filter measurement methods seem to be rather sensitive to the RH even if the RH is below the recommended value of 40%.
The results obtained for data corrected with the algorithm by Virkkula et al. (2007) were in many ways different from those obtained by Collaud Coen et al. (2010) who applied the Virkkula et al. (2007) correction to data from several stations in 5 Europe. They found that the compensation parameter (k) used in the algorithm was highly nonstable and that it led to large outliers. They correctly stated that the difficulty of applying this correction is due to the natural high variability of ATN as a function of time, which is for most of the time greater than the ATN decrease induced by filter changes. We therefore calculated 14-day running average compensation parameters (±7 days around each filter spot) in order to minimize these problems. The approach was obviously successful. It can be recommended that users of this method calculate running averages of k. However, 10 no exact time span can be given, it depends on the concentration level of the measurement siteat a clean site like SMEAR II 14 days was sufficient and in the polluted Nanjing 24 hours.
The results showed a great variation between the αabs derived from differently corrected σabs data and at SMEAR II the median αabs for different algorithms varied in the range of 0.93 -1.54. We also observed that most of the correction methods did not 15 prevent the change in the wavelength dependency as the filter got more loaded and therefore the αabs decreased notably with increasing attenuation (ATN). The correction algorithm by Virkkula et al., (2007) was the only AE31 correction algorithm, which produced a stable αabs for the increasing filter loading. For example, the αabs derived from Aethalometer measurements is often used to describe the chemical properties of the particles and to describe the source of black carbon. Not taking the used correction algorithm and the effect of increasing filter loading into account, could lead to wrong interpretation of the results. 20 According to our results, applying the Virkkula et al. (2007) correction algorithm could help solving if the changes in αabs were due to real variation or due to increased filter loading.
In general, the results showed that applying a filter loading correction to AE31 data clearly reduces the effect of increasing filter attenuation (ATN) and therefore applying a correction to the data is especially important, if the data is studied for shorter 25 periods. When applying a correction algorithm to AE31 data, it is important to report which algorithm, Cref values and other coefficients were used to acquire the final data product, since the algorithms can have a notable effect on the results, especially the absorption Ångström exponent αabs. Our results showed that it is a good practice to perform the analysis of AE31 data by using few different correction algorithms, to see if the results vary notably for different algorithms.