Determination of Aethalometer multiple-scattering enhancement parameters and impact on source apportionment during the winter 2017/18 EMEP/ACTRIS/COLOSSAL campaign in Milan

In the frame of the EMEP/ACTRIS/COLOSSAL campaign in Milan during winter 2018, equivalent black carbon measurements using the Aethalometer 31 (AE31), the Aethalometer 33 (AE33), and a Multi-Angle Absorption Photometer (MAAP) were carried out together with levoglucosan analyses on 12 h resolved PM2.5 samples collected in parallel. From AE31 and AE33 data, the loading-corrected aerosol attenuation coefficients (bATN) were calculated at seven wavelengths (λ, where λ values are 370, 470, 520, 590, 660, 880, and 950 nm). The aerosol absorption coefficient at 637 nm (babs_MAAP) was determined by MAAP measurements. Furthermore, babs was also measured at four wavelengths (405, 532, 635, 780 nm) on the 12 h resolved PM2.5 samples by a polar photometer (PP_UniMI). After comparing PP_UniMI and MAAP results, we exploited PP_UniMI data to evaluate the filter multiplescattering enhancement parameter at different wavelengths for AE31 and AE33. We obtained instrumentand wavelength-dependent multiple-scattering enhancement parameters by linear regression of the Aethalometer bATN against the babs measured by PP_UniMI. We found significant dependence of the multiple-scattering enhancement parameter on filter material, hence on the instrument, with a difference of up to 30 % between the AE31 and the AE33 tapes. The wavelength dependence and day–night variations were small – the difference between the smallest and largest value was up to 6 %. Data from the different instruments were used as input to the so-called “Aethalometer model” for optical source apportionment, and instrument dependence of the results was investigated. Inconsistencies among the source apportionment were found fixing the AE31 and AE33 multiple-scattering enhancement parameters to their usual values. In contrast, optimised multiple-scattering enhancement parameters led to a 5 % agreement among the approaches. Also, the component apportionment “MWAA model” (Multi-Wavelength Absorption Analyzer model) was applied to the dataset. It was less sensitive to the instrument and the number of wavelengths, whereas significant differences in the determination of the absorption Ångström exponent for brown carbon were found (up to 22 %). Published by Copernicus Publications on behalf of the European Geosciences Union. 2920 V. Bernardoni et al.: Aethalometer multiple-scattering enhancement parameters


Introduction
Light absorbing aerosols are of great interest for their effects: they provide a positive radiative forcing at global scale (IPCC, 2013) and can affect visibility at local scale (see e.g. Valentini et al. (2018) for estimates in Milan).
Black carbon (BC) and brown carbon (BrC) are major light absorbing aerosol species. They differ both in the extent of light 40 absorption per mass and its wavelength-dependence (Bond et al., 2013;Laskin et al., 2013). Furthermore, BC is a primary component and it is emitted in every incomplete combustion process. An important primary source of BrC is wood burning (e.g., Lack et al., 2013;Lu et al., 2015;Saleh et al., 2014;Washenfelder et al, 2015); recently, also other possible sources of BrC have been reported, e.g., BrC formation by secondary processes (Liu et al., 2015;Kumar et al., 2018). Mineral dust is another possible light absorber. At mid latitudes, its contribution is generally episodic and related to desert dust transport 45 episodes (e.g. Fialho et al., 2005).
Thus, aerosol absorption properties at different wavelengths are of interest not only to better characterise the interaction with solar radiation, but also as inputs to models for optical source apportionment using the Aethalometer model (Sandradewi et al, 2008) and for the identification of BC and BrC contribution to the absorption coefficient (component apportionment) using e.g. the Multi-Wavelength Absorption Analyzer model (MWAA model, Massabò et al., 2015). Nevertheless, it must 50 be recalled that particle absorption properties depend on particle size, composition, and mixing state. It is noteworthy that neither reference instruments (Bond et al., 2013;Moosmüller et al., 2009;Petzold et al., 2013) nor reference materials (Baumgardner et al., 2012) exist for the measurement of the aerosol absorption coefficient (babs). Thus, babs measurement and apportionment are still burning open issues in aerosol science.
Among the approaches for babs determination, filter-based measurements are widely used: indeed, filter-based automatic 55 instruments (able to operate for months with no need of maintenance) provide babs information with high temporal resolution with the advantage to obtain long-term data series of babs. Besides on-line devices, two off-line multi-wavelength instruments based on polar photometry were also developed in the last decade: the polar photometer PP_UniMI (Bernardoni et al., 2017a;Vecchi et al, 2014) and the Multi-Wavelength Absorption Analyzer MWAA (Massabò et al., 2013;Massabò et al., 2015). All filter-based measurements are affected by multiple-scattering effects as the aerosol is collected on fibre filters, and 60 by loading effects -i.e. non-linearities in light attenuation during filter loading (Liousse et al., 1993;Petzold et al., 1997;Bond et al., 1999;Moosmüller et al., 2009). Different approaches are used for the correction of loading and multiplescattering effects in filter-based instruments (e.g. Drinovec et al. 2015;Petzold and Schönlinner, 2004;Virkkula et al, 2007;Virkkula, 2010;Weingartner et al., 2003), and the details for those considered in this work will be explained in section 2.2.
As previously mentioned, despite the problems concerning babs measurements harmonisation, these data are used as input for optical source apportionment and component apportionment models. The most widespread among these models is the Aethalometer model (Sandradewi et al., 2008), which aims to apportion fossil fuel combustion (FF) and wood burning (WB) contributions to babs. For both sources, representative absorption Ångström exponent (αFF and αWB, respectively) are free 75 parameters of the model and have to be chosen a priori. Plenty of literature was spent on difficulties related to the choice of these parameters (e.g. Harrison et al., 2013, Fuller et al., 2014Helin et al., 2018, Martinsson et al., 2017, Zotter et al., 2017.
On the contrary, much less attention was dedicated to the role of the instrument providing the input data on the output of the Aethalometer model. Similarly, no investigation on the role of the instrument providing input data to the MWAA model for component apportionment is present in the literature. 80 This work tries to expand these fields and will show the results of the winter EMEP/ACTRIS/COLOSSAL campaign carried out in Milan in January and February 2018. Different filter-based on-line instruments were deployed (MAAP and Aethalometers mod. AE31 and mod. AE33), and sampling was carried out in parallel with 12-h resolution on quartz-fibre filters for the analysis by PP_UniMI. The work will show results about: -The assessment of multiple-scattering enhancement parameters at different wavelengths for AE31 and AE33 by 85 comparison with off-line measurements by PP_UniMI, including possible wavelength-dependence and daytime vs.
night-time differences.
-The role of input data provided by different instruments in the output of the Aethalometer model and MWAA model.

Aethalometers AE31 and AE33
The Aethalometers AE31 and AE33 perform on-line light-transmission measurements through a filter tape at 7 wavelengths (370, 470, 520, 590, 660, 880 and 950 nm). The output of both instruments at each wavelength (λ) is expressed as the concentration of equivalent black carbon (eBC(λ)) (Hansen et al., 1982;Petzold et al., 2013), as it is considered as the only 105 absorber. Being based on light transmission measurements only, the multiple-scattering effect (optical path enhancement induced by both the filter and the sample, making complicated accounting for both) and filter loading effects (non-linear optical path reduction induced by absorbing particles accumulating on the filter) (Weingartner et al., 2003;Arnott et al., 2005;Collaud-Coen et al., 2010) have to be accounted for to retrieve information on aerosol light absorption.
For both AE31 and AE33, linear relationship as in Eq. (1) is assumed between the loading-corrected attenuation coefficient 110 bATN and the absorption coefficient babs at a considered wavelength is assumed in the form: where C is named multiple-scattering enhancement parameter (see sections 2.2.1.1 and 2.2.1.2). The following paragraphs 115 provide details of the operation principles of both AE31 and AE33.

Aethalometer AE31.
The Aethalometer AE31 collects ambient aerosol on a spot on a quartz filter tape (Pall Q250 quartz) and measures the attenuation (ATN) at all available wavelengths: 120 where in Eq.
(2) I0 is the intensity of light transmitted through the blank filter spot and I is the intensity measured at a specific moment through the sampled spot. 125 To avoid the measurement of heavily loaded spot, the tape moves automatically to a fresh spot when ATN(370nm)=120.
(3) was dynamically determined following the Sandradewi et al. (2008b) algorithm. The present approach was recognised to be one of the best ones as corrected data are in good agreement with measurements from the MAAP and correction does not affect data in terms of the absorption Ångström exponent (Collaud Coen et al., 2010). Implementing corrections not affecting the absorption Ångström exponent is of great importance e.g. in heating rate studies; the approach mentioned above has been already applied successfully at the investigated site on data 140 series starting from 2015 (Ferrero et al., 2018) and it will be performed in the companion paper by Ferrero et al. (submitting) on the same dataset.
For these reasons, one the objective of this work is its experimental assessment exploiting PP_UniMI measurements as 150 explained in section 2.5. Considering that eBCAE31(λ) concentration is reported by the instrument at standard volumetric flow (20°C and 1013hPa). To allow comparison with PP_UniMI data (reported at ambient conditions and 12-h resolution), eBCAE31(λ) was firstly recalculated to the ambient flow conditions and then used to retrieve bATN_AE31(λ).

Aethalometer AE33 155
AE33 is the latest version of the Aethalometer. It collects ambient aerosol in parallel on two filter tape spots of the same area at different flowrates. In this work, the TFE-coated glass fibre filter tape T60A20 was used (Drinovec et al., 2015). Similarly to AE31, the tape is automatically moved to the fresh area of the tape to avoid heavily loaded spots. Highly time-resolved information on the light transmitted through the two spots at 7 different wavelengths is used to determine the loadingcorrected attenuation coefficient (bATN_AE33(λ)) in real-time using the "dual spot" algorithm described in Drinovec et al. 160 (2015).
(1), where CAE33_0=1.57 was suggested by manufacturer for the filter tape in use for harmonisation to AE31 data. 170 As eBCAE33(λ) data are reported by the instrument at standard volumetric flow (21.1 °C and 1013.25 hPa), bATN_AE33(λ) were referred to ambient pressure and temperature (12-h average) to allow comparison with PP_UniMI data.
As done for AE31, experimental investigation on the suitability of CAE33_0 was performed as explained in section 2.5. suitably corrected tri-color absorption photometer (TAP) babs,TAP measurements.

MAAP
The MAAP (637 nm, Müller et al., 2011) collects aerosol on a spot on a filter-tape and, as for the Aethalometers, the filter tape is suitably moved to avoid heavy loading when transmittance reaches a value that can be set by the user: in this work, default value (20%) was used. MAAP measures the light transmitted and scattered at fixed angles. Optimised analytical 180 functions are used to retrieve the total light in the front and back hemispheres by solid-angle integration (Petzold and Schönlinner, 2004). The MAAP algorithm implements a suitable radiative transfer model accounting for particle-filter matrix interactions (Hänel, 1987;Hänel, 1994). Results obtained using this method directly correct for multiple-scattering effects and are no issue related to filter loading was observed (Petzold et al., 2005).
As reported in Petzold and Schönlinner (2004), the input to this model are: 185 the ratios between the loaded and the blank spots analytical function integrals determined for the front and backward hemispheres, separately; backward-to-total light integral ratio for the blank filter matrix BM = 0.7 asymmetry parameter g = 0.75.
The raw outputs of the model are the optical depth (τ) and the single scattering albedo (ω) of the filter layer containing the 190 particles. The aerosol absorption coefficient (babs, expressed in Mm -1 ) in atmosphere during the sampling is determined considering the deposit area (A in cm 2 ) and the sampled volume (V in m 3 ) as in Eq.(5): 195 https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License.
Overall, a 12% uncertainty was reported (Petzold and Schönlinner, 2004). Assuming a constant mass absorption cross section (6.6 m 2 /g), the output of the MAAP is the equivalent black carbon concentration in air (eBCMAAP), expressed in μg/m 3 . Further details on the instrument are reported in Müller et al. (2011).

PP_UniMI analyses
The aerosol absorption coefficient at 4 wavelengths (405 nm, 532 nm, 635 nm, 780 nm) was determined on the collected 200 PM2.5 samples using the polar photometer PP_UniMI at the University of Milan (Vecchi et al., 2014, Bernardoni et al., 2017a. In PP_UniMI, the chosen laser beam hits the filter (either blank or loaded) perpendicularly. The filter transmits and scatters light in the front and back hemispheres. A photodiode mounted on a rotating arm scans the scattering plane (0-173° with about 0.4° resolution) allowing the determination of the total amount of light diffused in the two hemispheres by solid angle integration. 205 In usual PP_UniMI operation -hereinafter named "PP approach" (PP) -the same radiative transfer model as the one used in the MAAP is applied, but the following differences in input data evaluation have to be highlighted: front and backward hemisphere integrals are determined by solid angle integration of the high-angular resolution phase function measurements and not by analytical function integrals; no assumption on BM is done, as it is directly obtained by the measurements of the blank filter. 210 As well as for the MAAP, the outputs of the models are ω and τ. The minimum detection limits on the absorbance (ABS=(1ω)•τ) of the particle-containing layer of the samples are in the range 0.03-0.07 depending on the wavelength. It is also noteworthy that samples with ABS>0.9 were excluded by the database to avoid possible non-linearities due to sample overloading. Uncertainties were estimated in ±0.01 for ABS<0.1 and 10% for ABS ≥0.1 (Bernardoni et al., 2017a) It is noteworthy that exploiting information at suitable angles, the same approximations used in the MAAP calculation can 215 be implemented, i.e. total amount of light in the two hemispheres by analytical functions can be obtained, and BM=0.7 can be imposed, for the sake of comparison. This approach will be in the following referred to as "PP_UniMI as MAAP" (PaM) approach.
In both approaches (PP and PaM), the aerosol absorption coefficient at all PP_UniMI measurement wavelengths (babs,PP(λ) and babs,PaM(λ) for PP and PaM, respectively) can be obtained from ω and τ, considering the deposit area A=11.9 cm 2 and the 220 total sampled volume using Eq. (5). The comparison between the two approaches will be carried out through Deming linear regressions, as explained in section 2.8.

Levoglucosan measurements
After being analysed by PP_UniMI, one punch (1.5 cm 2 ) of each 12-h sample was devoted to the measurement of levoglucosan concentration. Each punch was extracted by sonication (1-h) using 5 mL ultrapure (Milli-Q) water. The 225 analysis was carried out by High-Performance Anion Liquid Chromatography coupled with Pulsed Amperometric Detection (HPAEC-PAD) at the University of Genoa following the procedure described in Piazzalunga et al. (2010). Minimum https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. detection limit for levoglucosan is about 2 ng/ml (i.e. 6.6 ng/m 3 considering the filter area and sampling volume) and uncertainties are ~11%.

Experimental absorption Ångström exponent 230
The experimental absorption Ångström exponent (αexp) was determined for each 12-h time slot from all instruments fitting the parameters Kexp and αexp in Eq. (6): It is noteworthy that light absorbing components (e.g. BC vs. BrC) have different λ-dependences and they both contribute to 235 αexp. Thus, it is not expected that Eq. (6) represents exactly the wavelength-dependence of the measurements (i.e. αexp is expected -and renown -to be dependent on the range of wavelengths considered in the calculation). Anyway, it is a good approximation and it can be exploited to gain information at wavelengths different from the measured ones (see e.g. application in section 2.5).

Optimisation of multiple-scattering enhancement parameters 240
Optimised multiple-scattering enhancement parameters at 4 different wavelengths for AE31 and AE33 (CAE31(λ), CAE33(λ), respectively) were retrieved by comparing loading-corrected attenuation coefficients bATN_AE33(λ) with the absorption coefficient measured by PP_UniMI, with both PP and PaM approaches (section 2.2), through a Deming linear regression analysis explained in section 2.8. When the intercept of the regression was comparable to zero, the slope of the regression line directly represented the best estimate for the corresponding multiple-scattering enhancement parameter. 245 To allow such comparison, PP_UniMI data were interpolated/extrapolated to Aethalometer wavelengths exploiting αexp calculated as explained in section 2.4 through the following relationships: babs(470nm)=babs(405nm)(470/405) -α exp babs(520nm)=babs(532nm)(520/532) -α exp babs(660nm)=babs(635nm)(660/635) -α exp 250 babs,(880nm)=babs(780nm)(880/780) -α exp It was already demonstrated for Aethalometer data that exploiting information at 370 nm or 470 nm for the evaluation of the absorption Ångström exponent has important impact on the result whereas information at longer wavelengths plays a minor role (Zotter et al., 2017). For these reasons, no extrapolation of PP_UniMI data at wavelengths shorter than 405 nm was performed; opposite, extrapolation was attempted at least at the nearer longer Aethalometer wavelength (i.e. 880 nm), as on 255 that side the curve is less steep and possible biases are expected to be smaller. https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License.
To ensure consistent comparison of the results at different wavelengths, only samples for which PP_UniMI information was available at all wavelengths were considered (i.e. samples in which measurements at all wavelengths were higher than LOD and with ABS<90).

Aethalometer model 260
The Aethalometer model was introduced by Sandradewi et al. (2008). Generally, the model is used to apportion the contribution of fossil fuel combustion (FF) and wood burning (WB) to both the aerosol absorption coefficient (babs) and carbonaceous fractions. In this work, we will focus on the babs source apportionment only. Please note that in this paragraph we will use babs with no explicit reference to the instrument used for its determination as it does not affect the explanation of the Aethalometer model itself. 265 The Aethalometer model exploits 2-λ babs measurements as input data and it is based on the following assumptions: at both wavelengths, FF and WB are the only sources contributing to the measured babs, as expressed in Eq.
where λ1 indicates a short wavelength, λ2 a long wavelength, and αFF is a parameter assumed a-priori, 275 representing the absorption Ångström exponent for the fossil fuel combustion source.
for wood burning it similarly holds Eq. (9): where αWB is another parameter assumed a-priori representing the absorption Ångström exponent for wood burning. 280 The identification of suitable αFF and αWB for the considered campaign/sampling site is recognised as the critical step in the modelling procedure and different approaches were proposed (e.g. Harrison et al., 2013, Fuller et al., 2014Helin et al., 2018, Martinsson et al., 2017, Zotter et al., 2017, Forello et al., 2019; opposite, less attention was posed to the role of using data from different instruments as input to the model. https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License.
However, once λ1, λ2, αFF, αWB are chosen, the babs source apportionment at λ1 and λ2 is carried out combining Eq. (7)  It is noteworthy that AE31 and AE33 provide 7-λ information, but the Aethalometer model represented by Eq. (7), Eq. (8), and Eq. (9) exploits information only at 2 chosen λs (from now on named "2-λ approach"). In this work, to exploit all the information provided by AE31 and AE33, we also propose an alternative approach, in the following named "multi-λ fit".
The multi-λ fit (regardless of the instrument) is based on Eq. (7) and keeps the Eq.(8) and Eq.(9) for fossil fuel combustion and wood burning contributions, but these dependences are extended to all wavelengths, thus considering Eq. (10): Multi-wavelength fit of equation (10)  Of course, the available wavelengths depend on the considered instrument, and it is also possible test the method using wavelength subsets. In this work, the whole available dataset (i.e. 4-λ: 405, 532, 635, 780 nm) was used as input for 305 PP_UniMI (both in PP and PaM approaches), whereas for the Aethalometers both the use of all the 7 available wavelengths and of the 4 wavelengths for which multiple-scattering enhancement parameters were determined (i.e. 470, 520, 660, 880 nm) were tested, to analyse the role of extreme wavelengths. It is noteworthy that using our multi-λ fit approach, it is possible to obtain the apportionment also at wavelengths different from the ones used as input (e.g. apportionment at Aethalometer wavelengths using as input the data by PP_UniMI). 310 Focusing on Aethalometers, for all the 2-λ and multi-λ fit approaches tested, input babs were obtained from Eq. (1) both using instrument-dependent C0 and optimised multiple-scattering enhancement parameters presented in section 3.3 and obtained as reported in section 2.5.
In all tests, besides relative babs(λ) source apportionment between FF and WB, correlation of babs,WB with levoglucosan (in terms of the Pearson correlation coefficient rWB) was tested. Since no tracer in atmospheric aerosol for fossil fuel combustion 315 was available, data on carbon monoxide (CO), nitrogen oxides (NOx) and benzene concentrations from the Regional Environmental Protection agency database were tested as possible tracers for traffic emissions, which dominate fossil fuel https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. babs contribution in Milan (Forello et al., 2019). Data were available at a traffic monitoring station at a distance about 2 km from our sampling site. Results of tests pointed to the benzene measurements at the traffic site as the best tracer for traffic, as it showed the highest correlation with babs,FF calculated for all instruments and calculation approaches (in terms of the 320 Pearson correlation coefficient rFF). Thus, correlation between benzene and babs,FF will be shown. It is noteworthy that, thanks to the features of the model, rFF and rWB do not depend on the choice of the considered λ for babs,FF and babs,WB, respectively.

MWAA model
The MWAA model (Massabò et al., 2015;Bernardoni et al., 2017b) allows to assess the contributions of BC and BrC to the total measured babs(λ) (component apportionment), and to provide information on the absorption Ångström exponent for BrC 325 (αBrC) exploiting Eq. (11): The coefficients A, B and αBrC in equation (11) are obtained by multi-λ fit of babs(λ) for each sample, provided that a value 330 for αBC is assumed a-priori. In this case, αBC=1 was chosen as already performed in previous applications (Bernardoni et al., 2017b, Massabò et al., 2015. Mathematically, at least 4-λ measurements are needed to fit 3 parameters. Nevertheless, tests evidenced problems in numerical calculation when using only 4-λ information (i.e. lack of convergence and/or fit parameter instability). Thus, in this work we used at least 5-λ information, consequently the MWAA model was run only using Aethalometer data as input. 335 The fit of Eq. (11) was performed considering both the whole datasets (7-λ) and excluding extreme values (i.e. 5-λ: 470, 520, 590, 660, 880 nm) to gain insight into the role of the information at extreme wavelengths on the results. Fixed multiplescattering enhancement parameters were considered, as the optimised ones were determined at 4-wavelengths only.
In section 3.3, the relative apportionment of the contributions from BC and BrC to babs(λ) was shown. As the main contributor to BrC is expected to be wood burning, the Pearson correlation coefficient (rBrC) between the apportioned 340 absorption coefficient for BrC (babs,BrC) and levoglucosan was also calculated. It is noteworthy that, as αBrC is different for each sample, rBrC depends on the considered wavelength. As BrC is expected to provide higher relative contribution at decreasing wavelength, rBrC was presented at the shortest wavelength available in all test -i.e. babs,BrC(470 nm) was used in rBrC evaluation.

Deming regression 345
In the results and discussion section (section 3), linear correlation between the data considered in the different comparisons were evaluated through the correlation coefficient r. https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License.
Linear regressions were performed using Deming regression (Deming, 1943;Ripley and Thompson, 1987). This approach is suitable when both data series are affected by not-negligible uncertainties (i.e. none of the series can be assumed as errorfree). The uncertainties associated to the data in the different cases will be described for each comparison. 350 The output of the Deming regression analysis will be represented in terms of slope, intercept, and their standard errors (SE).
When the intercept of the Deming regression line was comparable to zero within 3-times the standard error (3•SE), it was forced through zero: in the text it will be reported "the intercept was comparable to zero" and only the slope of the interceptforced regression will be presented. In the text and captions, "y vs. x" convention will be used (e.g. "PP vs. MAAP" means that in the regression PP_Unimi data obtained with the PP approach were displayed on y axis and MAAP data on x axis). 355

Comparison between MAAP and PP_UniMI results
The radiative transfer model used to account for multiple-scattering in the filter used for babs determination by PP_UniMI (see section 2.2.3) was run using as input both PP and PaM approaches. It is noteworthy that, while PP approach fully exploits highly angular-resolved measurements, PaM calculation introduces the same approximations as the ones used in the 360 MAAP -i.e. reconstruction by analytical functions from measurements at 3 angles and the fixed value between backward and total diffused radiation for blank filter BM=0.7 (section 2.2.2).
For each 12-h sample, babs,PP(635 nm) and babs,PaM(635nm) were compared to the average 12-h babs,MAAP (Figure 1). In both cases, high correlation is found (r > 0.991), and Deming regressions were performed with variance ratio = 1 (i.e. orthogonal regression) as data had comparable uncertainties (see sections 2.2.2 and 2.2.3). 365 When exploiting all the available angular resolved information in the PP approach, the intercept was not comparable to zero (-2.07 ± 0.47) and the slope was 0.928 ± 0.021. Nevertheless, comparing babs,PaM(635 nm) to the 12-h averaged babs,MAAP, the intercept was comparable to zero and the slope was 1.025 ± 0.011. The latter result confirms that PP_UniMI is equivalent to the MAAP when the same approximations were applied in calculation as performed in the PaM approach (section 2.2.3).
The previous comparisons also evidenced that the approximations implemented by the MAAP have a not-negligible impact 370 on the measured babs,MAAP. The individual role of the phase function reconstruction and imposition of BM = 0.7 is beyond the aim of the present work and it will be reported elsewhere (Valentini et al., in preparation), but first results indicate that the assumption on BM is the main responsible for the discrepancies. As for the presence of the intercept, this needs to be further investigated: scattering (Müller et al., 2011) or different penetration of the absorbers in the filter have been demonstrated to produce spurious absorption signals  at least for Aethalometers. 375

Comparison between PP and PaM approaches at all wavelengths
At wavelengths other than 635 nm, no comparison with MAAP is possible, thus only the comparison between the babs,PP(λ) and babs,PaM(λ) was performed. At all wavelengths, the results obtained were highly correlated (correlation coefficient r > https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. 0.993), but significant deviation from 1:1 relation was found, with PP results generally lower than PaM ones. Focusing on Deming regression line parameters (with variance ratio = 1), negative intercept was always found, whose absolute value 380 reduced with increasing wavelengths (see Table 1). In all cases, slope is not comparable to 1 within 3•SE.

Evaluation of multiple-scattering enhancement parameters for AE33 and AE31 during the campaign
PP_UniMI data were reported to Aethalometer wavelengths and used to gain information on multiple-scattering enhancement parameters for AE33 and AE31 at different wavelengths (CAE33(λ), CAE31(λ), respectively) as explained in 385 section 2.5. In the following, results will be presented by comparing loading-corrected 12-h averaged bATN(λ) from each Aethalometer to both babs,PP(λ) and babs,PaM(λ). This was done because PP results are obtained with less assumptions than those required by PaM approach. Nevertheless, PaM results were already demonstrated to be comparable to MAAP ones (section 3.1), thus C-values obtained with this approach are more directly comparable to data commonly obtained by research groups working with Aethalometers and MAAP in parallel for ambient measurements at urban or background 390 stations. The need to show both results highlights the importance of identifying a suitable reference material and reference instrumentation.
Very high correlation (r>0.98) was found at all wavelengths between Aethalometers bATN and both babs,PP and babs,PaM.
Deming regression was performed considering the following uncertainties: a constant 1 Mm -1 uncertainty was considered for all instruments, summed to 10% uncertainty for PP_UniMI and increased to 15% for Aethalometers (as the effect of variable 395 aerosol scattering coefficient on the measurements is not considered).
In Fig. 2, scatterplots of the AE33 data against both PP (left panels) and PaM (right panels) approaches were shown at the four wavelengths considered for comparison. In each scatterplot, lighter dots refer to daytime data, whereas the darker dots refer to night-time data. Deming regression line on the whole dataset (day and night data) was also shown. Intercept of the regression line was comparable to 0 at all wavelengths when calculated using the PaM approach data. In this case, the slope 400 of the regression line represented an average value for CAE33_PaM and resulted in the range 2.78≤CAE33_PaM(λ)≤2.93. These values are about 10% higher than CAE33=2.66 reported for Rome by  by comparison between AE33 and MAAP (with no wavelength adjustment). Considering the PP calculation approach, the intercept was not comparable to zero at 470 nm and 880 nm. Thus, we could provide CAE33_PP(λ) from the regression slope only at 520 nm and 660 nm: we found CAE33,PP(520 nm) = 3.53 ± 0.04 and CAE33_PP(660 nm) = 3.37 ± 0.05. It is noteworthy that the approach presented in Eq. (1) 405 neglects a possible additive contribution from scattering (i.e. is best at low single scattering albedo). The presence of an intercept not comparable to zero may indicate failure in such approximation. Furthermore, it has to be considered that few Mm -1 represent the limit of detection for PP_UniMI, thus it may have a role on the intercept.
Deming regression results were presented separately for daytime and night-time data in Table 2 for AE33. For these data, the intercept of the regression line was comparable to zero. Exceptions were PP night-time results at 470 nm and 880 nm for 410 which the intercept exceeded 3•SE for less than 10% and they were forced the same. Daytime CAE33(λ) values were higher https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. than the corresponding night-time ones, even if they were comparable within SE for both PP and PaM calculation approaches. More in detail, multiple-scattering enhancement parameters calculated with PP approach were in the range 3.41 ≤ CAE33,PP,day(λ) ≤ 3.57 for daytime dataset and 3.31 ≤ CAE33,PP,day(λ) ≤ 3.50 for night-time dataset; calculations with the PaM approach gave 2.79 ≤ CAE33,PaM,day(λ) ≤ 2.95 for daytime dataset and 2.77 ≤ CAE33,PaM,day(λ) ≤ 2.91 for the night-time dataset. 415 It is noteworthy that values at 470 nm and 520 nm are comparable within SE and the same occurs for the values at 660 nm and 880 nm for both PP and PaM approaches. Figure 3 provides the same representation already explained in Fig. 2, considering in this case the AE31 dataset. All intercepts of the Deming regression carried out on the whole AE31 data were comparable to zero. In this case, it resulted 3.47 ≤ CAE31_PaM(λ) ≤ 3.58 and these values were fully comparable to the suggested value of 3.5•(1 ± 0.25) (GAW, 2016). 420 Considering the PP approach, 4.22 ≤ CAE31_PP(λ) ≤ 4.33 was found. It is noteworthy that for both CAE31_PP(λ) and CAE31_PaM(λ), the values at different wavelengths were comparable within SE, thus no statistically significant λ-dependence was observed.
Focusing on daytime and night-time datasets, separately, also for AE31 daytime CAE31(λ) values were higher than the corresponding night-time ones even if they were comparable within SE, considering both PP and PaM calculation 425 approaches (see Table 3). More in detail, multiple-scattering enhancement parameters calculated with PP approach were in the range 4.34 ≤ CAE33,PP,day(λ) ≤ 4.44 for daytime dataset and 4.12 ≤ CAE33,PP,night(λ) ≤ 4.25 for night-time dataset; calculations with the PaM approach gave 3.55 ≤ CAE33,PaM,day(λ) ≤ 3.65 for daytime dataset and 3.39 ≤ CAE33,PaM,night(λ) ≤ 3.53 for the night-time dataset. For AE31, values at the different wavelengths were all comparable within SE for each approach, evidencing negligible λ-dependence. 430 It is noteworthy that all the CAE31(λ) values found comparing AE31 data with results by both PP and PaM approaches were higher than the corresponding values for AE33. This was expected, due to the different tape in use (recall CAE31_0=2.14 and CAE33_0=1.57 for the tapes in use).
Furthermore, multiple-scattering enhancement parameters calculated using babs,PP(λ) as reference measurement for the absorption coefficient were always higher than those obtained using babs,PaM(λ) as reference. This is due to the difference in 435 the results by the two approaches evidenced in section 3.2, related to the approximations performed by the MAAP in the evaluation of the input to the radiative transfer model (see sections 2.2.2 and 2.2.3).
Last, it is noteworthy that both for AE33 data in Table 2 and AE31 data in Table 3, PaM values are 17-18% lower than the corresponding PP values. This seems higher than the slope reported in Table 1 (about 0.87-0.88), but a not-negligible negative intercept is also present, thus the global difference between the approaches is indeed higher than the value given by 440 the slope.
These graphs immediately show that different λ-dependence is present in data from different instruments. 450 It is also of interest to gain insights into the effect of applying different multiple-scattering enhancement parameters to the data from AE31 and AE33 on the measured αexp. It should be recalled that in section 3.3 optimised multiple-scattering enhancement parameters were obtained at 470, 520, 660, 880 nm, only. So, αexp from AE31 and AE33 data were recalculated after evaluating babs(λ) from Eq. (1) only at 470, 520, 660, 880 nm, with the following choices for the multiplescattering enhancement parameters: 455 1) at all wavelengths C0_AE31=2.14, C0_AE33=1.57 were considered; 2) day-time and night-time wavelength-dependent multiple-scattering enhancement parameters C, reported in Table 2 for AE33 and in Table 3 for AE31 were used. Both PP-and PaM-derived multiple-scattering enhancement parameters were considered. These values will be in the following named "optimised multiple-scattering enhancement parameters". 460 Results of the αexp frequency distributions obtained from these tests were shown in Fig. 5.
It is noteworthy that Fig. 5a and Fig. 4c as well as Fig. 5b and Fig. 4d  The comparison of Fig. 5c and 5d to Fig. 4a as well as Fig. 5e and 5f to Fig. 4b, showed that the use of optimised multiplescattering enhancement parameters was not enough to harmonise the results of αexp from different instruments. There are different reasons for this. First of all, it is renown that experimental data are the sum of (at least) two contributions featuring different absorption Ångström exponents, thus the dependence is not expected to be exactly exponential; second, crosssensitivity to scattering is expected giving an additive term, which is neglected in the approach presented in Eq. (1) which 470 approximates the relationship between absorption and extinction by the use of a single multiplicative factor. Last, we are considering average factors and applying them to all the dataset, whereas sample-by-sample differences e.g. in the scattering properties of the particles are expected. Finally, it should be recalled that PP_UniMI wavelengths were 405, 532, 635 and 780 nm, whereas the wavelengths considered for Aethalometers 4-λ calculations were 370, 520, 660, and 880 nm.

Aethalometer model results 475
As mentioned in section 2.6, multi-wavelength information on the aerosol absorption coefficient can be used as input to the Aethalometer model for source apportionment. Section 3.4 showed differences in the λ-dependences of data from different https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. instruments, as well as the impact of considering fixed or optimised multiple-scattering enhancement parameters. These observations point to the need of investigating the role of such differences on source apportionment results. So, in this paragraph it will be investigated: 480 the role of performing the Aethalometer model using data from different instruments the impact of applying wavelength-dependent multiple-scattering enhancement parameters on the Aethalometer model source apportionment results.
In this work, the Aethalometer model was run applying αFF=1 and αWB=2. These values were previously used in Bernardoni et al. (2017b) for the Milan area during an application to a dataset with available wavelength information in the range 375-485 850 nm.
In the following, we will show results of the Aethalometer model run using as input data babs,PP(λ), babs,PaM(λ), and babs,AE31(λ) and babs,AE33(λ) obtained using both fixed multiple-scattering enhancement parameters and the optimised ones presented in section 3.3. Both the 2-λ and the multi-λ fit approaches (with all the possible combinations explained in section 2.6) were tested. A summary of the average apportionment, correlation coefficients between the apportioned wood burning babs,WB and 490 levoglucosan measurements (rWB), and correlation coefficients between the apportioned fossil fuel combustion babs,FF and benzene measurements (rFF) obtained with all the approaches was reported in Table 4.
From Table 4 and considering fixed multiple-scattering enhancement parameters for Aethalometers, it can be noted that: 1) Average apportionment percentage for AE31 and AE33 agreed within 7%, provided that the same short wavelength was used as reference (either 370 nm or 470 nm), regardless of the data processing approach. 495 Considering the same instrument, an average apportionment difference up to 12% was found at 470 nm for AE33 using 7-λ approach compared to 2-λ 470/950 nm. In any case, 7-λ apportionment is never in the range of variability found considering 470 nm as lowest wavelengths, still evidencing the impact of near-UV measurements on the source apportionment results.
2) Average PP_UniMI apportionment was within 6% considering all approaches, and within 3% considering 500 results from 4-λ fit. Thus, it should be mentioned that -even if we evidenced significant differences in absolute values for PP and PaM measurements in section 3.2 -such differences do not impact significantly PP_UniMI relative source apportionment.
3) Correlation coefficients rWB between babs,WB and levoglucosan showed high correlation (rWB≥0.92) for AE33 and AE31 results, independently of the approach; opposite, lower correlation was found with all the 505 PP_UniMI approaches (rWB≤0.83). Further investigation is needed to understand the reasons for this. This effect was possibly related to the wider αexp frequency distribution found in section 3.4 for PP_UniMI data.
Indeed, due to the fewer assumptions in babs retrieval, PP_UniMI seems more sensitive than Aethalometers to sample-by-sample variability. Consequently, the approach of the Aethalometer model based on fixing unique values of αFF and αWB for the whole dataset can make it less suitable to the application to such data. 510 Nevertheless, this needs further investigation e.g. using multi-wavelength Nephelometers in parallel to https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License.
Aethalometers to perform more accurate corrections of Aethalometer data. It should also be evidenced the role of a single point affecting the correlation. It does not result as an outlier looking at wavelength babs distribution, but its removal from the population increases rWB to 0.85-0.86, depending on the considered approach. 515 4) Correlation coefficients rFF between babs,FF and benzene are in the range 0.87-0.92 (being slightly higher for Aethalometers), showing lower dependence on the instrument and/or approach than rWB. Table 4 also allowed to perform comparison between Aethalometer apportionment obtained using fixed or optimised multiple-scattering enhancement parameters. As an example, considering input data in the range 470-880 nm, AE31 and AE33 babs,FF relative contributions at 470 nm were in the range 59-65% considering fixed multiple-scattering enhancement 520 parameters and 67-70% in the case of optimised ones; similarly, also considering other wavelengths for comparison, the ranges do not overlap. Thus, even if wavelength variabilities of multiple-scattering enhancement parameters were mostly within SE, they resulted in a significant impact on the average source apportionment results. Furthermore, PP_UniMI apportionments showed higher FF contributions than those obtained by AE31 and AE33 using fixed multiple-scattering enhancement parameters (up to 7% when considering 470 nm as lowest wavelength for Aethalometers and up to 17% when 525 comparing 7-λ fit on AE33, again evidencing the important impact of the shortest wavelength on the source apportionment); opposite, relative apportionment agreed within 5% at most (and, more in detail, PP_UniMI source apportionments results were always within the variability of Aethalometers results by different approaches) when optimised multiple-scattering enhancement parameters were considered for Aethalometers. This is an interesting result. Indeed, section 3.4 showed that the application of optimised multiple-scattering coefficient did 530 not lead to fully harmonised αexp frequency distributions. Nevertheless, here we showed that the use of optimised multiplescattering parameters can lead to the harmonisation at least of the average relative source apportionment.

MWAA model results
As explained in section 2.7, the MWAA model for component apportionment was run using as input both 7-λ and 5-λ AE31 535 and AE33 data. In Table 5, relative contributions of BC and BrC to babs(λ) obtained from the different tests was shown, together with αBrC (average ± standard deviation) and rBrC. Only Aethalometer wavelengths present also in Table 4 were reported. Table 5 showed that the component apportionment performed by the MWAA model is less sensitive to extreme wavelengths than the source apportionment performed by the Aethalometer model. Indeed, highest discrepancy of 5% in component 540 apportionment and rBrC≥0.91 were found at 470 nm in all cases. This was probably related to the ability of the model to selfevaluate the most suitable value for αBrC as a function of input data. This was supported by the investigation of the role of different input data (in terms of instrument and wavelength range) on the computed αBrC. In Fig. 6, frequency distributions of αBrC obtained in the different tests were shown: narrower distributions were obtained for AE33 than for AE31. This https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. observation held both for distributions obtained at 7-λ ( Fig. 6a and 6b) and at 5-λ ( Fig. 6c and 6d) and was confirmed 545 considering that standard deviations of αBrC values (Table 5) are 1.4 and 1.8 times higher for AE31 than for AE33. As for average αBrC values, the role of the considered instrument or number of wavelengths is unclear. Indeed, average αBrC obtained by AE33 data was 13% higher and 14% lower than those obtained by AE31 considering 7-λ and 5-λ, respectively. Furthermore, αBrC computed at 7-λ was 18% lower and 7% higher than the one computed at 5-λ for AE31 and AE33, respectively. 550 Furthermore, we exploited 4-wavelength babs(λ) measurements carried out off-line by PP_UniMI to determine optimised multiple-scattering enhancement parameters at different wavelengths for Aethalometers AE31 and AE33 -CAE31(λ) and 560 CAE33(λ), respectively -by comparison with loading-corrected bATN,AE31(λ) and bATN,AE33(λ). CAE31(λ) and CAE33(λ) were calculated using PP_UniMI data obtained by considering both the whole high-angular resolved information -babs,PP(λ), and using the approximations set in the MAAP -babs,PaM(λ). Considering all AE31 samples compared to the PaM approach, CAE31,PaM(λ) results were in the range 3.47-3.58 and were comparable to the values prescribed by WMO/GAW (3.5 ± 25%).

Conclusions
As for AE33, 2.78 ≤ CAE33,PaM(λ) ≤ 2.93 depending on the wavelength was found from the PaM approach. Nevertheless, PP 565 approach indicated that higher values (up to CAE31,PP(470nm)=4.33 and CAE33,PP(520nm)=3.53) can be more suitable, highlighting the role of MAAP approximations on the measured babs, but intercepts not comparable to zero were found in few cases, preventing the determination of an average value at 405 nm and 780 nm for AE33. This problem was overcome considering daytime and night-time data separately. In this case, daytime values of optimised multiple-scattering enhancement parameters were slightly higher than the night ones, but within the standard error, for both AE31 and AE33 as 570 well as using PP and PaM approach. Furthermore, also considering separately daytime and night-time data, values at different wavelengths were within SE for the same calculation approach. Separated daytime/night-time optimised multiplescattering enhancement parameters were used for further investigation.
The analysis of the experimental absorption Ångström exponents (αexp) evidenced that significantly different values were obtained depending both on the instrument and on the chosen wavelength-ranges from the same instruments. Wavelength-575 https://doi.org/10.5194/amt-2020-233 Preprint. Discussion started: 1 September 2020 c Author(s) 2020. CC BY 4.0 License. dependent multiple-scattering enhancement parameters determined in this work were also applied to data from AE31 and AE33, but they were not enough to harmonise αexp frequency distributions from different instruments.
This work investigated the role of such differences on the results of source apportionment by the Aethalometer model (by fixing a value of αFF=1 and αWB=2 already used in previous works in the area) and of the component appotionment by the MWAA model (fixing αBC=1). The Aethalometer model was applied using as input babs data determined by PP_UniMI, 580 AE31 and AE33. As for AE31 and AE33, babs(λ) obtained both using fixed and optimised multiple-scattering enhancement parameters were used as input. The role of different choices for the considered wavelength was also investigated, as well as different calculations approaches. Inconsistencies in relative source apportionment were found also considering a single instrument, evidencing not only the role of the chosen wavelength range (already found in the literature) but also that small differences (within uncertainties) in the wavelength-dependencies of multiple-scattering enhancement parameters affect 585 significantly the output of the Aethalometer model. Significant differences were found between the apportionment results from PP_UniMI data and those obtained by AE31 and AE33 with fixed values for the multiple-scattering enhancement parameters. It is noteworthy that the application of optimised multiple-scattering enhancement parameters did not harmonise αexp frequency distributions among different instrument, but it led to consistent source apportionment results.
Focusing on the MWAA model, due to the features of the model our tests were limited to the assessment of the role of 590 extreme wavelengths on the model results for AE31 and AE33. The average apportionment of the relative contributions of BC and BrC from AE31 and AE33 showed little influence on the considered wavelength range (5% maximum, to be compared to 11% limiting Aethalometer model analysis to the tests comparable to those performed by the MWAA model).