Aerosols measurements were performed at Barcelona (BCN; urban background; 41∘23′24.01′′ N, 2∘6′58.06′′ E; 80 m. a.s.l.), Montseny (MSY; regional background; 41∘46′46′′ N, 2∘21′29′′ E; 720 m a.s.l.) and Montsec d'Ares (MSA; mountaintop; 42∘3′5′′ N, 0∘43′46′′ E; 1570 m a.s.l.) monitoring supersites (NE Spain). As shown later, these stations are characterized by aerosols with different physical and chemical properties that influenced the differences obtained in the C values. A detailed characterization of the three measurement stations can be found in previous works (e.g. , for BCN; , for MSY; , for MSA). Briefly, the BCN station is located within the Barcelona metropolitan area of nearly 4.5 million inhabitants at a distance of about 5 km from the coast. The MSY station is located in a hilly and densely forested area, 50 km to the N–NE of Barcelona and 25 km from the Mediterranean coast. The MSA station is located in a remote high-altitude emplacement on the southern side of the Pre-Pyrenees at the Montsec Range, 140 km to the NW of Barcelona and 140 km to the WNW of MSY. These supersites are part of the Catalonian Atmospheric Pollution Monitoring and Forecasting Network and of the ACTRIS and GAW networks. Aerosol optical properties at the three sites were measured following standard protocols (WMO/GAW, 2016).

The area of study is characterized by high concentrations of both primary and secondary aerosols, especially in summer from diverse emission sources. Anthropogenic emissions from road traffic, industry, agriculture and maritime shipping, among others, strongly contribute to the air quality impairment in this region . Moreover, the Mediterranean Basin is also highly influenced by natural sources, such as mineral dust from African deserts and smoke from forest fires among others.

The different analyses were performed considering the absorption coefficients provided by either the MAAP or PP_UniMI as reference absorption measurements depending on either time resolution and coverage or the measurement availability at several wavelengths. The AE33 and MAAP data (provided with a high temporal resolution) were used to study the seasonal variations and the cross-sensitivity to scattering of the C factor. The AE33 and PP_UniMI data (provided with a low temporal resolution but at different wavelengths) were used to determine the wavelength dependence of the C factor.

The cross-sensitivity to scattering of the C factor at the three stations was obtained by analysing the relationship between the multiple-scattering parameter C (at 637 nm) and the measured SSA (Eq. ).

The SSA was obtained independently at 637 nm using simultaneous MAAP and multiple-wavelength integrating nephelometer data. C was obtained through Eq. () from the AE33 attenuation coefficient, extrapolated at 637 nm using the absorption Ångström exponent (AAE) from AE33 and the MAAP absorption coefficients at 637 nm. The analysis was performed by binning the SSA data using criteria and then averaging the obtained C values within each SSA bin. Binned data were then fitted following Eq. () to obtain the experimental values of both Cf and ms.

Figure  and Table  show the results of the fit for BCN, MSY and MSA for both M8020 and M8060 filter tapes. Moreover, Table  compares the C values obtained here with those reported in the literature for the M8020 filter tape. For M8020, we calculated a constant Cf of 2.21±0.01 and a cross-sensitivity to scattering, ms, of 1.8±0.1 at MSY and of 1.96±0.02% and 3.4±0.1 % at MSA. For the M8060 filter tape, the fit yielded a multiple-scattering constant Cf of 2.50±0.02 and a cross-sensitivity to scattering of 1.6±0.3 % at BCN, a Cf of 1.96±0.01 and a ms of 3.0±0.1 % at MSY, and a constant Cf of 1.82±0.02 and a ms of 4.9±0.1 % at MSA.

As a consequence of the cross-sensitivity to scattering, we can appreciate in Fig.  a clear increase in C with increasing SSA with an up-to-3-fold increase in C for SSA>0.90–0.95 depending on the station and filter tape considered. The cross-sensitivity to scattering was evident for both filter tapes at the regional (MSY) and mountain (MSA) stations where the probability of measuring SSA higher than 0.90–0.95 was high (57 %–70 % of the data in Fig. ). Conversely, at the urban site (BCN), where the SSA was on average lower (12 % of SSA data were above 0.90), a lower cross-sensitivity to scattering was observed. This significant increase in the C factor at high SSA, if not accounted for, can lead to a large overestimation of both eBC concentrations and absorption coefficients from Aethalometer instruments. This effect can have a larger impact at sites where high SSA values are typically observed such as remote Arctic sites and mountaintop sites , as well as in places where increasing or decreasing trends of SSA have been observed . This cross-sensitivity to scattering of the filter explains the higher C factors obtained on average at these types of sites (Table ) and suggests the need to use either a site-specific C value or a C value that takes into account the SSA measured by an independent absorption method. Given its impact on the absorption coefficient, this effect needs to be taken into account for climate studies.

In order to further characterize the observed cross-sensitivity to scattering, we explored how the variations in C with SSA depended on different intensive aerosol particle optical properties, namely the AAE (Fig. S3), backscatter fraction (BF, Fig. S4) and single-scattering albedo Ångström exponent (SSAAE, Fig. S5). We found that large C values and high SSA were often obtained when the sampled aerosol composition was dominated by mineral dust during Saharan dust outbreaks, as demonstrated by the occurrence of negative SSAAEs at high SSA (Fig. S5). In fact, Saharan dust outbreaks, which are common in the WMB , have the potential to increase the SSA above the average values especially at the regional (MSY) and remote (MSA) stations e.g.. In prior studies, negative values of the SSAAE have been associated with an aerosol mixture dominated by mineral dust . Moreover, we observed that high C values (for SSA>0.95) were also associated with AAE values higher than around 1.5 (see Fig. S3), thus indicating a relatively higher absorption efficiency of the collected particles in the UV, consistent with the presence of either dust or brown carbon (BrC) particles . Furthermore, low BF values, indicative of the predominance of large particles, were also on average associated with high SSA values (see Fig. S4). Note that the dependence of C vs. SSA on the aforementioned intensive optical properties was not clearly observed in BCN, where, at least for the period under study, local pollution masked the effects of coarse dust particles on the measured intensive optical properties and on SSA which kept values lower than around 0.90–0.95. The observed dependency of C on intensive aerosol particle optical properties demonstrated that both particle size distribution and chemical composition can affect the reported C-vs.-SSA relationships.

Here we present the average values and the seasonal cycle of the C factor calculated at 637 nm at BCN, MSY and MSA. We analysed the multiple-scattering parameter C values both through a Deming regression, taking into account the measurement error in the MAAP 12 %; and in the AE33 15 %;, and by calculating the median value of the C-factor density distribution. The uncertainties in the C factor were derived as either the methodological error from the regression slope of the Deming fit or the half width at half maximum (HWHM) of the density distribution of the C factor. We present here the results from both the aforementioned methods because both methods have been reported in the literature (e.g. ; see Table  in this work).

The density distribution of the C factor obtained from the ratio (with a variable time resolution, as mentioned in Sect. ), showed a quasi-Gaussian distribution at the three measurement sites with a small tail towards higher C values (Fig. ).

The median values of the C factor for the M8020 filter tape were 2.29±0.48, 2.29±0.46 and 2.36±0.59 for BCN, MSY and MSA, respectively. These values were on average similar or slightly lower (with differences less than 7 %) compared to the median C values obtained for the M8060 filter tape of 2.44±0.57, 2.23±0.30 and 2.51±0.71 (see Table ). The Deming regression fit results (Fig. S6) showed C values of 1.99±0.02, 2.05±0.02 and 2.21±0.03 (at BCN, MSY and MSA, respectively) for M8020 which were slightly lower (with differences <10 %) compared to the C values of 2.20±0.02, 2.13±0.01 and 2.05±0.02 obtained for M8060. Note that the uncertainties from the Deming regression were lower compared to the uncertainties derived as the HWHM of the distributions because the Deming regressions were performed using binned data (see Fig. S6). This also was the likely explanation for the lower C values on average obtained with the Deming regression compared to the median values of the density distribution. The difference in the C values between both methods ranged between 4 %–18 % depending on the filter tape/measurement station considered (see Table ). However, both methods were consistent and provided a higher C factor for the M8060 than for the M8020 filter tape.

As reported in Table , overall, higher C values were found at MSA, where both the SSA and the cross-sensitivity of the filter tape to scattering were higher compared to at MSY and BCN (see Figs.  and S7). The C values for the AE33 M8020 and M8060 filter tapes obtained at urban background stations in Rome and Leipzig were in the same range as those found in this work for BCN (Table ).

Figure  shows the seasonal variability in the C factor for the TFE-coated glass and M8060 filter tapes at the three stations. The large variability in the obtained C parameters (see Fig. ) at the three sites during all the seasons, consistent with the width of the C-factor density distribution (Fig. ) and the SSA seasonal evolution variability (Fig. S7) can be appreciated.

On average, an increase in C was observed at MSY and MSA in summer (JJA) for both filter tapes. This increase was likely driven by a greater influence of diurnal processes and the impact of the atmospheric boundary layer (ABL) during the warm months at these two elevated stations and by changes in the chemical and physical properties of collected particles in summer compared to in winter (DJF). In fact, spring and summer seasons in the WMB are characterized by a high frequency of Saharan dust outbreaks e.g. and the formation of high concentrations of secondary organic aerosols and secondary sulfate particles e.g. which in turn increase the particle scattering efficiency and the SSA in summer compared to in winter . Although dust particles can absorb radiation e.g., the effect of Saharan dust outbreaks at the measurement stations considered here was to increase the SSA (at 637 nm) over the average values. In fact, as shown by , both scattering and absorption increased at MSY and MSA during Saharan dust outbreaks, but the resulting SSA was higher compared to other atmospheric scenarios typical of the area under study. Therefore, the higher C values observed during Saharan dust outbreaks were coherent with an increase in SSA over the threshold above which C sharply increased (see Figs.  and S3–S5). An increase in C when dust particles are deposited on the filter tape was also reported by for the AE31 Aethalometer. reported C values for dust particles by generating particles by mechanical shaking of dust samples from different desert soils using AE31 and MAAP measurements, and they reported C values of between 3.6 and 3.96 for Saharan soils Table 2 of.

As shown in Sect. , high SSA increased the C values, and, consequently, the C seasonality was affected, to some degree, by the SSA seasonality. In fact, Fig. S7 shows that the seasonal evolution of the SSA at MSY and MSA mirrored quite well the seasonal evolution of C, with an increase in both C and SSA towards the warm season. In BCN, the inter-season variability in both C and SSA was less pronounced and C remained fairly constant during the different seasons. An exception was in the winter period (DJF) when both C (M8060) and SSA showed minima. Nevertheless, the variability within each season was the largest in BCN, due to a higher variability in the SSA values at this station within each season compared to in MSY and MSA (Fig. S7). The relationship between C and SSA can be also observed in Fig. S8, where the diel cycles of both C and SSA were reported. In BCN, both C and SSA showed two relative minima in the morning and in the afternoon, mirroring the traffic rush hours. At MSY, the sea-breeze-driven transport of pollutants in the afternoon caused a reduction in both SSA and C. Conversely, at MSA both C and SSA showed less variability in the diel cycles and less similarity was observed. Note that the similarities commented on above between the diel/seasonal cycles of C and SSA were more or less evident depending on the season/station considered. In fact, we have shown in Fig.  that high SSA (>0.90–0.95) can strongly affect the C values, but less dependency between C and SSA was observed for lower SSA, thus also contributing to masking the similarities between C and SSA reported in Figs. , S7 and S8, which were obtained averaging all available data, including C values at lower SSA.

The spectral dependence of the AE33 C factor, C (λ), was studied at the three stations by comparing the attenuation coefficients, batn, from AE33 at seven different wavelengths with the absorption coefficients, babs, from PP_UniMI. To this aim, the PP_UniMI absorption coefficients were interpolated and extrapolated to the seven AE33 wavelengths using the absorption Ångström exponent (AAE) obtained from the original PP_UniMI measurements. The obtained mean AAE were 1.12±0.17, 1.29±0.24 and 1.35±0.18 for the BCN, MSY and MSA stations, respectively, with an increase from the urban (BCN) to the regional (MSY) and remote (MSA) sites due to the increase in the relative importance of non-fossil BC sources (e.g. biomass burning) and Saharan dust at the remote sites compared to BCN.

Figure  shows that at the urban (BCN) and regional (MSY) stations the C factor did not present a statistically significant dependence on the wavelength. However, Fig. c shows that at the remote MSA station the multiple-scattering parameter C presented a statistically significant increase between 370 nm (C=3.47) and 950 nm (C=4.03) (see Table S2). The observed increase in the C factor with wavelength affects the absorption coefficients derived from the AE33 attenuation measurements and, consequently, can affect all the intensive optical parameters such as the AAE, SSA and SSAAE which can be derived from the multi-wavelength AE33 absorption measurements and scattering coefficient measurements. Moreover, a wavelength-dependent C factor can impair Aethalometer-based BC source apportionment analysis, such as that of the Aethalometer model, used to determine the contribution from fossil fuels vs. biomass burning emissions . Contradictory results have been reported in the literature about the spectral dependence of C for older versions of the Aethalometer (model AE31). For example, found a strong indication of the independence of C from the wavelength, and did not find any wavelength dependence of the multiple-scattering parameter C. Conversely, observed a decrease in the C factor with wavelengths, although it was not statistically significant.

As can be appreciated by comparing Figs. –, the multiple-scattering correction factors obtained using the PP_UniMI reference instrument were larger than those obtained with the MAAP as a consequence of the offset in the absorption measurements between the MAAP and PP_UniMI. A detailed discussion of this offset can be found in Fig. A1 and in Fig. 2 in .

Hereafter, we propose a possible explanation for the different spectral dependencies found for C at the measurement sites considered here. We have shown in Sect.  that, independently from the measurement station considered, the cross-sensitivity to scattering can strongly increase C for SSA values above an upper threshold. To explore if the SSA can also affect the C wavelength dependence, we studied the wavelength dependence of C for SSA values above and below the site-dependent SSA thresholds. Figure  shows the comparison between the C factor at MSY and MSA for SSA above (high SSA) and below (low SSA) the SSA thresholds of 0.95 and 0.9, respectively, for MSY and MSA (see Fig. ). Figure  shows that at MSA there was a statistically significant increase in C with the wavelength for SSA>0.90, whereas no statistically significant increase was observed for SSA<0.90. For this specific analysis, based on the PP_UniMI off-line measurements, 86 % of SSA values at MSA (68 samples out of 79) were above the SSA threshold of 0.95. At MSY, only 1 sample out of 126 was characterized by an SSA value higher than the SSA threshold of 0.95, thus preventing a robust statistical analysis of the C wavelength dependence for high SSA at MSY. Despite this, a 17 % increase in C with the wavelength, from 2.85 at 370 nm to 3.43 at 950 nm, for this single point was observed (see Fig. a). At MSY, similarly to MSA, C did not show any dependence on the wavelength for SSA<0.95 (see Fig. c). Thus, this analysis demonstrated that a high SSA of the particles deposited on the filter tape can increase the C values, influencing at the same time their wavelength dependence.

We have shown in Sect.  that the sharp increase in C at high SSA at the stations herein analysed can be associated with the presence of particles dominated by dust, characterized by low SSAAEs and BFs and high AAEs and SSA (Figs. S3–S5). Therefore, we performed a similar C spectral dependence analysis to that in Fig.  but separating the days affected by Saharan dust (dust) from the days without dust influence (no-dust). As shown in Fig. , no spectral dependence of C was observed during either dust or no-dust scenarios at MSY. This lack of dependence on the dust intrusions could be due to the limited number of off-line samples at MSY characterized by high SSA (1 out of 126). Thus, due to the low temporal resolution of off-line PP_UniMI measurements, even during Saharan dust days the SSA at MSY rarely increased above the SSA threshold. Nevertheless, using high-time-resolution data (see Fig. ) the potential effect of dust particles to increase the SSA (and consequently C) was evident at both MSY and MSA. At MSA (see Fig. ) C showed a statistically significant increase with wavelength for both dust and no-dust samples due to the fact that the samples with high SSA at MSA (86 %) were well distributed between the two scenarios. Thus, these results confirmed that the SSA was the main parameter that influenced the spectral behaviour of the C parameter.

To further explore the possible causes that contributed to the different C spectral dependencies observed, we performed a similar analysis to that in by comparing C and its wavelength dependence with different intensive aerosol particle optical properties, namely the SSA, BF and SSAAE. and have shown that the AE33 factor loading parameter, k, increases with an increasing BF (smaller particles) and decreases with increasing SSA and that the wavelength dependence of k also depends on these two optical properties as well as on the particle mixing state. In Fig. S9 in the Supplement we present a similar analysis by studying the effects of these intensive optical properties on the multiple-scattering parameter C instead of on k. Figure S9 shows the slope of C with the wavelength (i.e. the wavelength dependence of C) with the SSA, BF and SSAAE at the three sites. No clear relationship was observed between the C slope and the three intensive optical properties at both BCN and MSY. Moreover, the C slopes at these two sites were close to zero for the considered intensive optical properties. The observed lack of a C gradient was again likely due to the fact that at BCN and MSY the SSA did not exceed the threshold value, even when the SSAAE indicated the possible presence of Saharan dust intrusions at MSY (see Fig. S9h). However, Fig. S9c shows that at MSA there was a shift of the C slope towards large positive values when SSA was above 0.95. Below this SSA threshold value, the C slope was close to zero, confirming the reduced C wavelength dependence for low SSA values at MSA. Moreover, when the SSAAE (BF) at MSA (see Fig. S9i and f) decreased towards negative (low) values (Saharan dust intrusions), the slope of C increased, again confirming the potential of coarse Saharan dust to increase the SSA and, consequently, C especially at the remote site. Note that, as already commented on (see Fig. ), the C slope also kept positive values at MSA for the samples not dominated by dust (SSAAE>0), thus further indicating the predominance effect of SSA on the C wavelength dependence. Thus, the results presented in Fig. S9 confirm the effects of SSA on C presented in Figs.  and .

The lack of points for BCN (none) and MSY (1 of 126) for large SSA values, especially above the SSA threshold obtained in Fig. , prevented extrapolating the results to other measurement background conditions, and further studies should be performed to better characterize the spectral behaviour of C and its dependency on the cross-sensitivity to scattering under different atmospheric conditions/scenarios. This is especially important, as already commented on, in view of the contradictory results reported in the literature e.g.. The results presented here clearly indicated that when the SSA exceeded a given site-dependent threshold, as determined using the method in Sect. , the C values and their wavelength dependence increased. For the measurement sites considered here, Saharan dust outbreaks were identified as a possible cause for SSA values higher than the threshold. However, from a general point of view, other factors, including the location of the measurement stations and/or absence of anthropogenic pollution, can determine the presence of a particle mixture with high or very high SSA.

Finally, we performed a sensitivity study on the effects that using a wavelength-dependent C (C(λ)) had on the AAE derived from AE33 measurements, comparing the results with those obtained using the usual approach based on the application of a constant C factor (C(const)). Figure  shows that the AAE values for BCN and MSY did not present any significant variation (see Table S4), with AAE mean values of 1.19±0.15 and 1.27±0.12 (at BCN and MSY, respectively) for C(const) and 1.17±0.15 and 1.25±0.12 (for BCN and MSY, respectively) for C(λ). These results for BCN and MSY were coherent with the observed lack of spectral dependence of C at these two stations (Fig. ). However, at MSA the observed increase in C with the wavelength introduced an increase into the AAE of around 13 %, from 1.19±0.07 (C(const)) to 1.35±0.07 (C(λ)). Similarly, Fig. S10a and b present the results of a sensitivity analysis performed to understand the effects that using a constant or a wavelength-dependent C had on the SSA at 470, 660 and 950 nm. As with the AAE, Fig. S10c shows no significant variation in SSA at the three considered wavelengths at BCN and MSY, again consistent with the observed lack of dependence of the C factor on the wavelength at these two sites. However, Fig. S10 shows a statistically significant increase in the SSA at the MSA station of around 1.3 % at 660 nm and 2 % at 950 nm when using C(λ) instead of C(const). Conversely, as expected, no statistically significant change was appreciated at the lower wavelength, 470 nm. This variation introduced by C(λ) into the AAE and SSA, although not large, is relevant since it occurs at the threshold of the SSA value for which a substantial increase in C as a function of SSA is observed, as shown in Sect. .