The actual aerosol light absorption coefficient of the initially suspended particles is not σ0. When aerosol particles deposit onto a filter, they will inevitably interact with the filter. The realisation of this has resulted in a variety of different data-processing correction schemes for the Aethalometer and the PSAP (Arnott et al., 2005; Bond et al., 1999; Collaud Coen et al., 2010; Schmid et al., 2006; Virkkula et al., 2005, 2007; Weingartner et al., 2003). The purpose of these corrections is to derive the actual light absorption coefficient (σap) of the suspended particles devoid of filter-induced artefacts.

The Arctic measurement sites included in this study all have the same type of measurement instrument, namely the Aethalometer model AE31, except for Summit, which is an AE16 model Aethalometer. The benefit of having the same type and model of instrument is that measurement artefacts for the same type of instrument would be expected to be more similar than between different types of instruments. The comparison of aerosol properties between different sites should be more robust when all sites have the same type of instrument than if the instruments would differ from site to site. Both the AE31 and AE16 model use the same type of filter (Pallflex Q250F). However, it still has to be acknowledged that artefacts can differ between different stations depending on the difference in aerosol properties even though the same type of instrument is used.

For the sake of inter-comparability, a relative normalisation factor is introduced to harmonise the determination of the absorption coefficient at the Arctic stations. The harmonisation factor is calculated as Cf=σ0σap, where σap is the light absorption coefficient as measured by co-located filter-based absorption measurements. The co-located instruments are discussed in more detail in the next section. The interpretation of the correction factor is in essence how much greater the attenuation coefficient is in comparison to the light absorption coefficient of the co-located filter-based absorption photometers which have been corrected for loading and scattering artefacts. Thus, Cf will effectively be an inter-instrument comparison factor.

This correction factor can be used in many of the available correction algorithms in the place of the multiple scattering correction factor (Cref); see Collaud Coen et al. (2010) Table 2 for a list. However, the Cf values reported here are not multiple scattering correction factors because no true reference absorption measurements were available. The purpose of the Cf values here is to provide a general value that can be used in place of the Cref value for the Arctic, in order to harmonise the determination of σap from Aethalometers in the Arctic with other methods for determining aerosol light absorption coefficients.

The Arctic sites in this study were chosen based on the criterion that they all have Aethalometers and an additional co-located filter-based photometer measuring aerosol light absorption coefficients. The additional instrument is either a MAAP, PSAP, or CLAP. These instruments will provide the σap that is needed to calculate Cf for the sites, using Eq. (3). The MAAP is a filter-based absorption instrument that, in addition to transmittance measurements through the filter, also measures the back-scattered light at two angles (Petzold and Schönlinner, 2004). This allows for a radiative transfer scheme to be applied since the back-scattered light at multiple angles can be used to distinguish between diffusely scattered light and Gaussian scattered light. This information is then used to calculate the diffuse fraction of light scattered back by the filter in order to account for multiple scattering and apparent absorption effects by solving the radiative transfer equation from the measurements on the filter.

The PSAP and CLAP instruments measure transmission, and therefore are based on Eqs. (1) and (2). Both instruments use the same type of filter, and the optical design of the CLAP is very similar to the PSAP. The CLAP differs from the PSAP in that, instead of a single sample spot on a 10 mm filter, it has eight sample spots on a 47 mm filter. Solenoid valves are used to switch to the next sample spot once the filter transmittance reaches 0.7. Thus, the CLAP can run 8 times as long as the PSAP before requiring a filter change, which is ideal for remote sites that are not visited daily.

Both the PSAPs and CLAPs use the same type of Pallflex E70-2075W filters, with the only difference being their size. As the optical designs of the two instruments are very similar, both the PSAP and CLAP data used in this study were corrected using the Bond et al. (1999) correction along with the Ogren (2010) wavelength adjustment. It has been shown before that the same type of filter and a similar optical design yields very similar results (Miyazaki et al., 2008; Nakayama et al., 2010). The Bond et al. (1999) correction includes a multiple scattering correction, a filter loading correction, and an apparent absorption correction. The apparent absorption correction makes use of light scattering coefficients (e.g. from nephelometers). At all sites in this paper where light scattering coefficients were needed to correct the PSAP and CLAP, the light scattering was measured by TSI nephelometers (TSI Inc, model 3563; Anderson and Ogren, 1998).

Although the co-located instruments are based on collecting the sample aerosol on filters, there are differences. For aerosol particles that have a high single-scattering albedo (ω0), defined as the ratio of light scattering (σsp) to light extinction (σep), the MAAP has been shown to be less prone to interpret light scattering as light absorption than a PSAP or an Aethalometer (Petzold et al., 2005). In the Arctic, this is an advantage because of the high ω0 of the aerosol. Research has also shown a good agreement between the MAAP and independent reference absorption (σep–σsp) measurements for ω0 values in the range of 0.7–0.98 (Sheridan et al., 2005). The same study also showed that the PSAP, with the Bond correction applied, agrees better with independent reference absorption measurements for atmospherically relevant ω0 values (0.88) than for very dark aerosol (ω0=0.30). At a ω0 of 0.88, there was virtually no dependence of filter loading on σap. MAAP-, PSAP-, and CLAP-derived σap will be cross sensitive to σsp for a purely scattering aerosol, and the extent of the cross sensitivity depends on the loading of the filter (Müller et al., 2011).

The unit to unit variability of the MAAP is comparatively lower than for the other absorption photometer instruments used in this study (Müller et al., 2011). The same study also showed that the instrument noise of the PSAP and the MAAP are lower than for Aethalometers. The design of the PSAP and CLAP instruments should also make the measured flow through the instruments less uncertain than in instruments using a filter tape roll because the filters are sealed in place inside the instrument.

It should be noted that none of the filter changes for any of the instruments can be considered to be synchronised with each other; e.g. the PSAP filter is not changed at the same time as an Aethalometer tape advance. Thus, when comparing a reference instrument to an Aethalometer, using the whole time series, any remaining cross sensitivity to the state of the filter on a reference instrument will represent the mean or median bias.

Because the reference instruments operate at different wavelengths than the Aethalometers, Ångström exponents (α) were used to interpolate or extrapolate data to a matching wavelength; α were also used to match nephelometer wavelengths to reference absorption wavelengths when using the correction schemes. The Ångström exponent was calculated as follows: α=-log(σ1)-log(σ2)log(λ1)-log(λ2), where σ1 and σ2 represent absorption or scattering coefficients at their respective wavelengths λ1 and λ2. Using α, the absorption coefficient (σx) can be calculated for a desired wavelength λx using σx=σ1λ1λxα.

Using Eqs. (4) and (5), the Aethalometer data was interpolated to the wavelengths 467, 525, and 637 nm. The reference absorption instruments that did not already measure at these wavelengths were also interpolated to these three wavelengths. The 1-wavelength Aethalometer at Summit was interpolated from 880 to 637 nm using an α of 0.814 in Eq. (5).

Aethalometers that are deployed in clean environments can appear at times to just be reporting noise. By simple data post-processing, the signal can be extracted with a greater accuracy, albeit at the expense of temporal resolution (Hagler et al., 2011). This can be done by allowing for a temporal resolution that matches the concentration of species that creates the instrument response, namely the change in ATN, by choosing a constant relative uncertainty (Eq. 8). Equation (8) states that when fq and fa are constant, the relative uncertainty depends on the change in filter attenuation (ΔATNND). This fact can be used to produce a time series with a constant relative uncertainty.

However, it should be acknowledged that there is an additional uncertainty due to instrument drift, but in principle a constant uncertainty could also be achieved using Eq. (7). That would require a thorough investigation into the sources for the drift and how they vary between stations, which is not feasible in this study given the remote locations of the stations. However, based on the laboratory measurements the drift can be significant on a timescale from hours to days. When the aim is to determine the drift at a station, the absolute filter should be attached to the sampling line to capture the pressure changes in the sampling line relative to ambient pressure, and changes in relative humidity, on a pristine filter. This could possibly be extended to include loaded filters for different aerosol types and filter loadings.

The measurement uncertainties for the six Aethalometers at the respective stations were determined by measuring particle-free air. For all stations except Alert, particle-free air was sampled for at least 24 h with an absolute filter connected to the instrument inlet. These measurements are shown in Fig. 3 at a wavelength of 590 nm (Summit 880 nm). For Alert, the particle-free air was sampled for a few hours per week comprising 4 days of data in total.

Figure 3 depicts the ATN drift in the different Aethalometers during the particle-free air measurements. The figure shows that all the tested Aethalometers experienced drift during the particle-free air measurements. Also evident from the figure is that the drift of the different Aethalometers (and different sites) can differ. Based on the figure, it is not enough to conduct measurements on particle-free air for a few hours in order to assess the instrument performance at the site. Filtered air measurements should instead be performed over a period of 24 h or more. These measurements should be conducted on a pristine filter to minimise the influence of semi-volatile constituents that could have been deposited onto the filter (Cappa et al., 2008; Lack et al., 2008).

For reference, a linear drift of ΔATND=1.0 in 24 h is shown in Fig. 3, which corresponds to a σ0 value of 0.07 Mm-1 when using Q= 5 L min-1, A=0.5 cm2, and Δt= 24 h. The consequence of a linear drift of 1.0 in 24 h would also set the lowest value achievable. As can be seen from the inserts of Fig. 1, ATND needs not be increasing all the time, and thus lower values of σ0 are achievable during periods with little drift. It should be mentioned that this drift will also affect the eBC concentrations reported by the instrument. For the five instruments evaluated here, the drift uncertainty is shown in Fig. 3 to be roughly 0.01–0.1 Mm-1.

The particle-free air measurements were not all conducted in the same manner, which is both fortunate and unfortunate. Figure A2 in Appendix A shows the zero air measurements for ATN in greater detail. The Aethalometers at Alert, Barrow, Tiksi, and Pallas were not connected to the common aerosol inlet at the sites but drew air from inside, through a low resistance absolute filter. Again, this setup should only result in a negligible lower pressure in the sampling line after the filter. The most intriguing of the zero air measurements is Tiksi. Similar to Fig. 1, Tiksi shows abrupt changes in ATN that cannot be related to pressure changes in the sampling line. One of the abrupt changes occurred at night when there was no personnel at the station (see Fig. A2). The Tiksi Aethalometer also shows uneven drift, when compared to other channels, for the 370 and 950 nm channels that cannot be explained with aerosol deposition onto the filter. The hypothesis is therefore that this is electronic drift. Changes in filter morphology or position should affect all wavelengths. The Tiksi Aethalometer also has a noisy 880 nm channel which is clearly visible in Fig. A2.

Pallas, Zeppelin, and Summit all experienced drift immediately following the change to a pristine filter although the drifts were quite different. For Pallas, the drift was observed as a gradual and increasing ATN. The drift was largest for 370 nm at both Pallas and Zeppelin but not in the same very clear trend breaking way that was observed at Tiksi; although at Zeppelin the 370 nm channel behaved somewhat differently than the other channels. At Summit, the ATN changes were faster although smaller in magnitude. Again we hypothesise that these changes in ATN during the particle-free air measurements can be due to deposition or evaporation, or both, of semi-volatile organic compounds or changes in sample air relative humidity. The decreasing ATN at Zeppelin could be due to evaporation of adsorbed water or organics from the filter. At Barrow, the zero air measurements were conducted on a loaded filter. After an absolute filter was placed before the instrument, ATN started to drop. Possible causes can be the evaporation of organics or water vapour. It is possible that the absolute filter changes the partial pressure of one or more gas-phase constituents that subsequently affect the ATN. The rapid changes in the Barrow ATN values correlate well with rapid fluctuations in the sampling line temperature which is exposed to room air and therefore also to the air-conditioning unit. The ATN values increased when room temperature was dropped and vice versa.

The standard deviations of the ΔATNND measurements made with an absolute filter in line are shown in Table 2. Because the only wavelength-dependent variable in Eq. (8) is δΔATNND, the change in the ΔATN measurements with respect to wavelength will also be the sole source of the difference in the relative uncertainty between different wavelengths. The values that describe the relative uncertainty in terms of Δt and σ0 (Eq. 10) are presented in Table 3.

Figure 4 shows the relative uncertainty (δσ0/σ0) of Eq. (8) as a function of ΔATNND based on measurements conducted with an absolute filter upstream of the instrument. For clarity, the figure was produced using a mean of all wavelengths to represent the typical relative uncertainty of the instrument. The mean values were calculated from Table 2. Figure 4 shows how the relative uncertainty decreases when ΔATN increases. The upper x-axis scale of σ0 in the figure was calculated for reference using Q=5 L min-1, A=0.5 cm2, and Δt=60 min.

Implicit from both Fig. 4 and Eq. (8) is that the relative uncertainty of the instrument changes with the aerosol concentration when using a fixed Δt; for a fixed Δt, ΔATN will change according to the concentration. The equation for the relative uncertainty (Eq. 8) can be used as a criterion to achieve a more constant level of uncertainty which was not captured when the method was introduced by Hagler et al. (2011). This can either be determined from Fig. 4 directly or calculated from Eq. (8) after the term δΔATNND has been determined.

One way to characterise the performance of an Aethalometer is to calculate the ΔATN value at which the flow (fq) and spot size (fa) uncertainties together are equally important as the ΔATN uncertainties. This is shown in Table 4. The crossover was calculated by solving ΔATN from the terms under the square root of Eq. (8), namely ΔATNND=(δΔATNND2/(fa2+fq2)2)1/2. The uncertainty in the flow rate, relative to the uncertainty in the ATN measurements, diminishes exponentially when ΔATN decreases (Fig. 4). Here, a criterion of ΔATN ≥ 2 was used in the post-processing of the data to also allow for a lower detection limit in the boxcar-averaged reference data that is discussed in the next section.

For the sake of simplicity, this criterion was only applied to the middle wavelength of the Aethalometer (590 nm). If the criterion were to be applied to all wavelengths, one would end up with seven time series for each instrument, with different timestamps. That could make further data analysis unnecessarily convoluted. It is worth pointing out that if the data set being analysed is going to be averaged, then the ATN values included with the averaged data set should not be averaged – an averaged ATN would make Δt less well defined. Instead, either the first or the last ATN value during the averaging period should be incorporated into the averaged data set.

The time series of the 1 h boxcar-averaged Aethalometer data is show in Fig. 5. The time series of the adaptive collection time is shown in Fig. 6. When using the adaptive collection time, it is clear that when the absorption coefficient is low, the time resolution is low. At higher absorption coefficients, the time resolution is better. This is desirable since it means that at high concentrations of light absorbing aerosol particles there is no loss in temporal resolution, whereas at low concentrations this adaptive method is capable of reaching lower detection limits quicker than boxcar averaging when drift is minimal.

Comparing Figs. 5 and 6, it is clear that the adaptive collection time approach is to be favoured when σap<0.1 Mm-1 because of instrument noise. In Fig. 5, it is shown that at low σap the 1 h averages of the data set are clearly more scattered than when using the adaptive collection time method when σap is low (Fig. 6). Since the y-scale of Fig. 5 is logarithmic, negative values are not shown, although they are still present in the 1 h averaged time series. By definition, the adaptive collection time approach will not produce negative σ0 values since ΔATN is always positive.

In fact, for the measurements studied here, when the σ0 is above 2.1–6.7 Mm-1, there is no loss in the temporal resolution in the 1 h averaged data of Fig. 5. The range in σ0 is due to the fact that the different Aethalometers at these six Arctic sites are operated at different flow rates. Figure 7 shows histograms of Δt for the different stations using the adaptive collection time approach.

Figure 6 shows values that are lower than the example drift in ΔATN = 1.0 in 24 h (Fig. 3), which implies that there are periods where the drift can be substantially lower. In Figs. 5 and 6, the σap values come from σ0 values that have been corrected using a Cf value of 3.45 as discussed in the next section. Thus, the drift uncertainty seen in Fig. 3 becomes 0.003–0.03 Mm-1 after Cf is applied.

The determination of the Aethalometer correction factor for the Arctic was done according to Eq. (3). For the calculations, σ0 values were obtained using the collection time approach because a constant relative uncertainty is desirable. The collection time approach applied to the Aethalometer data impacts the co-located absorption photometer data as well. The collection times for the Aethalometers were adapted to ΔATN. Subsequently, data from the co-located instruments were boxcar-averaged to the same time intervals as the Aethalometer data in order to calculate Cf. The co-located instruments will therefore have a longer averaging during times when σap is low, given that σap and ΔATN correlate. For standard boxcar averaging, random measurement noise reduces proportionally to tavg-0.5 (e.g. Springston and Sedlacek, 2007). Using the collection time approach, δσ0 can at best be reduced at a rate of Δt-1.0 (Fig. 2).

Applying uncertainty propagation on Eq. (3) yields δCfCf=δσ0σ02+δσapσap2. The term δσ0/σ0 is discussed in this work and cannot be lower than the spot sizes and flow rate uncertainties. This also holds true for the co-located absorption photometers. Equation (12) also implies that the relative uncertainty of Cf increases when σap and σ0 are low if the absolute uncertainties δσap and δσ0 remain constant. Using ΔATN to determine the averaging time for σap will lower δσap proportionally to tavg-0.5. For non-drift situations, the adaptive collection time approach will reduce δσ0 at a rate of Δt-1.0, which is faster than boxcar averaging and desirable because Aethalometers are generally more noisy than PSAPs and MAAPs. For reference, the PSAP and MAAP absolute uncertainties are typically 0.02 and 0.06 Mm-1 for 5 min averages (Müller et al., 2011). The 5 min PSAP absolute uncertainty was calculated from 0.05 Mm-1 for 1 min averages using a tavg-0.5 dependency. These absolute uncertainties of the PSAP and MAAP are much lower than the Aethalometer uncertainties shown in Table 3.

The uncertainty of Cf is greater than the uncertainty that originates in measurement noise. Filter-based absorption photometers are generally considered to be accurate to within 20–30 % of the true σap value (Bond et al., 2013). The accuracy is a combination of electronic noise, instrument variability, and calibration uncertainty (e.g. Sherman et al., 2015). The adaptive averaging time approach will only lower measurement uncertainties from electronic noise and not the uncertainties associated with the measurement technique itself.

The Cf values presented here can be used in many of the existing Aethalometer correction algorithms in the place of the multiple scattering enhancement factor. However, Cf values calculated here should be viewed as a harmonising correction factor for the Arctic Aethalometers to the co-located filter-based absorption photometers and not as a literal multiple scattering enhancement factor.

There are several possible issues with the derivation of Cf values presented here. First, in this study, the co-located absorption photometers also rely on measurements using filter-based absorption techniques – it remains unclear to which extent this will affect the absolute values of Cf because no absorption standard measurements were available at the sites. However, since the filter changes of the different instruments are not synchronised, and because the data sets cover 3 years at each site, it can be assumed that there is very little coincidence with respect to filter loading effects. Thus, the Cf values presented here should represent typical values for the different sites. This argumentation should especially hold true for a moderately loaded filter, e.g. ATN < 10. Second, the flow rates of the different instruments differ, which can affect the Cf values due to different penetration depths (Lack et al., 2009; Nakayama et al., 2010). Third, it has to be acknowledged that there can be a bias in the absolute Cf values because of imperfect corrections of filter artefacts in the reference instruments (Backman et al., 2014; Müller et al., 2011). However, this bias should not fundamentally alter the ATN dependency because filter changes were not performed in sync. The reasoning is elaborated on in Appendix B. As the filter gets loaded with aerosol particles, loading effects come into play. These loading effects change between the filter spots depending on the optical properties of the aerosol that is being deposited on that particular spot (Virkkula et al., 2015) and even during sampling on the same spot (Drinovec et al., 2015).

Such detailed analysis of filter loading effects is not feasible with this data set since it would require data with a high temporal resolution and preferably concurrent non-filter-based light absorption measurements. In general, the goodness of evaluation for all filter-based light absorption measurements should be the continuous light absorption coefficients over filter spot changes so that a filter spot change would go unnoticed; this should hold true for all aerosol types and loadings. This means that there would not be an ATN dependency when compared to non-filter-based light absorption measurements.

It has been shown that published Aethalometer correction algorithms, which aim to compensate for filter loading and multiple scattering effects, do not necessarily remove the ATN dependence when applied on data from different stations (Fig. 4 in Collaud Coen et al., 2010). Again, the aim is not to add another correction algorithm to literature. Instead, the Cf values presented here should be interpreted as a means to make Aethalometers in the Arctic more inter-comparable by introducing a Cf value for the Arctic using the co-located absorption photometers.

Figure 8 shows the calculated Cf values as a function of ATN for the six Arctic sites. Since the data depicted in Fig. 8 were produced using a concentration-adapted collection time, the statistics in the figure were calculated using a collection-time-weighted percentile (Hyndman and Fan, 1996). Without this weighting, the statistics would have effectively been concentration weighted. Figure 8 is equivalent to Fig. 4 of Collaud Coen et al. (2010) for the values labelled “AE manufacturer” in their figure.

In general, Tiksi and Pallas show the highest Cf values, whereas Summit shows the lowest. Summit stands out as an outlier in Fig. 8; it is the station at the highest elevation and uses a 1-wavelength Aethalometer (880 nm). The Summit Aethalometer data were interpolated to a wavelength of 637 nm using an α of 0.814 obtained from the co-located 3-wavelength CLAP. A summary of the different Cf values calculated for the stations is presented in Table 5.

In addition to the different Cf values observed over the ATN range in Fig. 8, there are other differences among the stations. Some of the Cf values decrease as a function of ATN. In the ATN range of 0–10, the median Cf values for Alert and Tiksi are greater than at the other stations, but at higher ATN the Alert and Tiksi Cf values decrease. This is an expected behaviour and is due to the filter loading effect causing a decrease in Aethalometer sensitivity. However, a decrease in Cf with ATN is barely noticeable for the Barrow and Zeppelin data sets, although the variation in Cf at Zeppelin makes the trend – or lack thereof – less clear.

Again, Summit shows a different behaviour altogether. As the filter ATN increases, so do the Cf values. This is contrary to the expected behaviour of the filter loading effect in which loading generally decreases the sensitivity of a filter-based absorption measurement technique (Arnott et al., 2005; Virkkula et al., 2007). The filter loading effect is most pronounced for an aerosol with a low ω0 (Sheridan et al., 2005). The fact that Summit does not follow this trend suggests that the aerosol optical properties of Summit are different in relation to the other stations. The different behaviour, however, does not seem to be related to ω0 as the ω0 of Summit does not stand out.

The scattering Ångström exponent (αsp, Eq. 4) is shown in Fig. 8. The αsp of an aerosol is indicative of aerosol particle size with values below unity indicating super micron aerosol, and values close to 4 indicate a predominantly fine-mode aerosol. Only the nephelometers at Pallas and Summit are connected to PM2.5 inlets, with the rest connected to PM10 inlets. Thus, both Pallas and Summit have smaller aerosol particles than the rest of the stations according to αsp and very similar ones when compared with each other. If the PM2.5 inlet were to be the reason for a lower Cf at Summit, then Pallas should also have to be influenced since the MAAP at Pallas is behind a PM2.5 inlet. Also shown in Fig. 8 are aerosol back-scatter fractions (b) which are related to the size of the aerosol and have been shown to affect Aethalometers (Virkkula et al., 2015). The site that resembles Summit the most, considering αsp, b, and ω0 is Pallas. The Pallas Aethalometer was operated with a filter change interval of 8 h for most of the time, and therefore there are very few data points with an ATN above 10. Hence, it is questionable whether there are enough data to be able to draw conclusions about a trend in the Cf and ATN relationship for Pallas.

Also shown in Fig. 8 are the slopes (k) of the ATN dependence. The slopes were calculated by linear regression to match the equation σap/σ0=1+k⋅ ATN that follows the notation of previous work (Virkkula et al., 2007, 2015). It is well known that light scattering by particles affects filter-based absorption photometers, which wrongly gets interpreted as light absorption, termed apparent absorption. For the co-located PSAP and CLAP instruments, this has been compensated for by subtracting a fraction of the light scattering from the light absorption (Bond et al., 1999; Ogren, 2010). For the co-located MAAP instruments, scattering correction is applied by the firmware (Petzold and Schönlinner, 2004). These corrections need not be enough for all types of aerosols, and a cross sensitivity to light scattering can remain (Müller et al., 2011). For σ0, no scattering correction has been applied.

Figure 9 shows Cf as a function of σsp. Since no scattering correction has been applied to σ0 the expected behaviour is that σ0 increases with σsp. This seems to be the case for Alert, Summit, Barrow, and Zeppelin, with a clearer trend for Alert and Barrow. All stations that show an increasing trend of Cf with σsp have a co-located PSAP or a CLAP. It is possible that the non-compensation of σsp on σ0 is further influenced by a too-large or too-small compensation of σsp on σap. Since σap is the denominator of Eq. (3), an overcompensation of apparent absorption would also cause Cf to increase with σsp. Both stations that have a MAAP as the co-located instrument show a decreasing Cf as σsp increases.

Another possible explanation for a changing Cf with σsp can be that different levels of σsp are associated with different aerosol types and therefore also Cf. Different levels of pollution can be associated with different sources of pollutants. These different sources could have different chemical and physical properties that could impact the Cf ratio. The right hand y axis in Fig. 9 shows the median ω0 of the aerosol for the range of σsp. The Cf value seems to follow the general trend of ω0 so that when ω0 increases, so does Cf. It is not clear whether this is due to measurement artefacts or a difference in aerosol properties. The fact that the same behaviour is observed in Tiksi and Pallas indicates that the cross sensitivity to ω0 is not restricted to the PSAP and CLAP instruments.

In the upper part of Table 5, it can be seen that there is not much variation in the Cf values at different wavelengths. In the table, the Aethalometer data were interpolated using Ångström exponents to match the wavelength of the reference instruments using Eqs. (4) and (5). It cannot be ruled out that the low variability in Cf with wavelength is a consequence of the co-located instruments used. No multi-wavelength long-term measurements of aerosol absorption coefficients from non-filter-based measurement instruments were available. The lower part of Table 5 provides statistics of Cf for each site. Because there does not seem to be a great wavelength dependence on the Cf value at Alert and Barrow, the Cf value for all wavelengths was calculated using all available wavelengths. The overall value of Cf for sites across the Arctic was determined to be 3.45. The value of 3.45 was calculated using average-time weighted median as discussed earlier, and the weighted 25th and 75th percentiles for the all wavelength Cref values are 2.93 and 4.15, respectively. Because Summit appears to be significantly different from the other Arctic stations, the Summit Cf was omitted from the grand median Cf calculation.

Figure 10 depicts the relationship between the reference absorption instrument (σap) and σ0 which yields Cf; see Eq. (3). The figure is provided as an overview comprising all wavelengths and all stations except for Summit, because of the reasoning mentioned before. In the figure, in addition to the weighted median value of 3.45, the slope of the bivariate fit is also shown. The fit was performed using bivariate regression with the averaging time as weights (Cantrell, 2008). The slope of the bivariate regression becomes 3.59 (standard error 0.01). Both the regression method and the weighted median method yield values that are within 3 % of each other. The root-mean-square error (RMSE) was calculated from the predicted σ0 using the results from the regression, which becomes 1.14 Mm-1.

The mass absorption cross section (MAC) describes the relationship between eBC mass concentrations and σap. Similarly, MACAE describes the relationship between σ0 and eBC as given by the manufacturer; both MAC and MACAE have units of m2 g-1. A simple evaluation can be performed to investigate whether the Cf value is reasonable, assuming that the difference between MACAE and MAC is Cf (Arnott et al., 2005). If the Aethalometer measured at a wavelength of 550 nm, then MACAE would be 26.59 m2 g-1. Compensating MACAE with Cf=3.45 would yield a MAC of 7.7 m2 g-1, i.e. a MAC which is 3.45 times lower than MACAE. This MAC is within the range suggested by Bond and Bergstrom (2006), namely 7.5 ± 1.2 m2 g-1 at 550 nm, which implies that the Cf value determined here is reasonable. This simple evaluation, however, does not take into account any apparent absorption or coating effects.

Multiple scattering correction factors (Cref) have been reported for a range of different sites around the world. Although the Cf values reported here cannot be considered to be equivalent to multiple scattering corrections, it is still useful to compare Cf with Cref. Cref values reported in the literature are summarised in Table 6.

Some of the variations in the reported Cref values of Table 6 can be attributed to the different ways in which they were calculated. Some Cref values were calculated with a filter loading correction applied and some without. Moreover, some of the Cref values were calculated with both a scattering and a filter loading correction applied. For the sake of inter-comparability, a Cref value calculated without any of the available correction algorithms would be preferable.

Comparing the grand median Cf value of 3.45 conceived here shows that it is well within the range of studies reporting Cref values. The values that are the closest are those by Collaud-Coen et al. (2010), which is not surprising since that study had light absorption coefficients from a MAAP as reference and not true reference absorption measurements. The Cf value of 3.45 conceived here is also close to 3.5, which is what the Global Atmospheric Watch's World Calibrations Centre for Aerosol Physics recommends using globally (GAW Report No. 227; http://wmo-gaw-wcc-aerosol-physics.org/wmo-gaw-reports.html).