Determination of the multiple-scattering correction factor and its cross-sensitivity to scattering and wavelength dependence for different AE33 Aethalometer filter tapes: A multi-instrumental approach

Accurate measurements of light absorption by aerosolized particles , especially black carbon (BC), are :::::::: Providing ::::::: reliable :::::::::: observations :: of ::::::: aerosol ::::::: particles ::::::::: absorption ::::::::: properties :: at ::::: spatial :::: and :::::::: temporal ::::::::: resolutions ::::: suited :: to ::::::: climate :::::: models :: is : of utter importance since BC represents the second most important climate-warming agent after carbon dioxide (CO2). Reducing the uncertainties related to the absorption measurement techniques will improve the global estimation of BC concentration and the 5 radiative effects of light absorbing aerosols. Currently : to ::::: better ::::::::: understand ::: the :::::: effects ::: that :::::::::: atmospheric ::::::: particles ::::: have :: on ::::::: climate. :::::::: Nowadays, one of the :::::::::: instruments most widely used instruments for BC and absorption measurements is the :: in ::::::::::: international ::::::::: monitoring :::::::: networks ::: for :::::: in-situ :::::: surface :::::::::::: measurements ::: of :::: light ::::::::: absorption ::::::::: properties :: of ::::::::::: atmospheric :::::: aerosol :::::::: particles :: is ::: the :::::::::::::: multi-wavelength : dual-spot aethalometer, AE33, which . :::: The :::::: AE33 derives the absorption coefficients of aerosol particles at 7 different wavelengths from the measurements of optical attenuation ::: the :::::: optical ::::::::: attenuation ::: of :::: light through a filter where 10 particles are continuously collected. An accurate determination of the absorption coefficient ::::::::: coefficients ::::: from ::::: AE33 ::::::::: instrument relies on the quantification of ::: the non-linear processes related to the collection of sample ::::: sample ::::::::: collection on the filter. The multiple-scattering correction factor (C(λ)), which depends on the filter tape used and on the optical properties of the collected particles, is the parameter with ::: both : the greatest uncertainty ::: and ::: the :::::: greatest :::::: impact ::: on ::: the :::::::: absorption :::::::::: coefficients :::::: derived ::::: from :: the :::::: AE33 :::::::::::: measurements. 15 An :::: Here ::: we ::::::: present :: an : in-depth analysis of the AE33 multiple-scattering correction factor :: C and its wavelength dependence for different :: two :::::::: different ::: and :::::: widely ::::: used filter tapes, i.e. the oldmost referenced known as :::::: namely: ::: the :::: old, ::: and ::::: most ::::::::: referenced, : TFE-coated glassand the current : , :: or ::::::: M8020, :::: filter :::: tape :::: and ::: the :::::::: currently, ::: and : most widely usedM8060, has been

measurements networks. Filter-based instruments (either on-line or off-line) rely on the sampling of aerosol particles collected in a filter matrix and on the measurement , with a photometer, of the resulting change of light intensity ::: with :: a ::::::::: photometer, either on the transmittance (Hansen et al., 1984;Bond et al., 1999;Drinovec et al., 2015), or on both transmittance and reflectance (Petzold and Schönlinner, 2004). This method is affected by artifacts resulting mainly from the effects that the filter has on the 90 measurements. Off-line in-house made filter based polar photometers, which measure both transmittance and reflectance, are deployed at some research centers. Examples are the MWAA (multi-wavelength absorption analyzer) deployed at University of Genoa (Massabò et al., 2013) and the PP_UniMI polar photometer deployed at University of Milan (Vecchi et al., 2014;Bernardoni et al., 2017). These methods can perform accurate absorption measurements by increasing the number of measuring angles (Massabò et al., 2013;Vecchi et al., 2014;Bernardoni et al., 2017) thus allowing an accurate determination of the filter 95 artifacts.
The filter loading effect consists in the accumulation of particles and the consequent loss of sensitivity of the instrument with an increasing particle load (Bond et al., 1999;Weingartner et al., 2003;Lack et al., 2008;Moosmüller et al., 2009). The crosssensitivity to scattering is the consequence of the multiple light scattering within the filter fibers and between particles and fibers, thus it is largely dependent on the single scattering albedo of the deposited aerosols. For the older Aethalometer model 115 (AE31) the filter loading effect has been thoroughly studied and different methods for its quantification have been suggested.
These methods use for example the discontinuity between the eBC concentration measurements before and after a filter spot is changed (Weingartner et al., 2003;Virkkula et al., 2007), : or use the relationship between the eBC concentration and light attenuation (Park et al., 2010;Segura et al., 2014;Drinovec et al., 2015) to correct for filter loading effect. For the AE33 model the loading effect is corrected on-line using the dual-spot technology (Drinovec et al., 2015). In addition, the different physical 120 and chemical properties of the collected particles influence particle optical properties : , such as the backscatter fraction and the single scattering albedo (SSA), thus affecting also the multiple scattering of the collected particles and the filter loading effect (Weingartner et al., 2003;Lack et al., 2008;Virkkula et al., 2015;Drinovec et al., 2017). Among the on-line filterbased instruments, the Multi Angle Absorption Photometer (MAAP) uses also ::: also :::: uses : the measurements of light scattered by the blank and loaded filter : in ::::: order : to take into account for both the loading effect and the aerosol particles multiple 125 scattering. Consequently, the MAAP directly provides particle absorption coefficients similar to those obtained with other types of instruments (e.g. PAS; Petzold and Schönlinner, 2004;Petzold et al., 2005).
Therefore, it is often taken as the reference in inter-comparison exercises with other instruments, such as the AE33 e.g. in Backman et al. (2017). The discrepancy between MAAP and PP_UniMI reported by Valentini et al. (2020b) was mainly attributed to the value of the fraction of backscattered radiation set in the MAAP algorithm and directly measured by PP_UniMI thanks to the ::: due :: to ::: its high angular resolution which scans the whole scattering plane (resolution of 0.4 degrees in the scattering 155 angle range 0-173 • ). Valentini et al. (2020b) also reported no differences between MAAP and PP_UniMI when the PP_UniMI was used with the same assumptions as those used in the MAAP (PaM as defined in Valentini et al., 2020b).

Aerosol absorption and eBC measurements
The on-line aerosol absorption coefficient, b abs , was measured at the three sites with a multi angle absorption photometer (MAAP, Model 5012, Thermo, Inc., USA, Petzold and Schönlinner, 2004) ::::::::::::::::::::::::::::::::::::::::::::::::::: (MAAP, Model 5012, Thermo Inc., USA, Petzold and Schönli This instrument derives the absorption coefficient at 637 nm (Müller et al., 2011a) and eBC concentration using a radiative transfer model from the measurements of transmission of light through the filter tape and backscattering of light at two different 205 angles. eBC ::::: Black :::::: carbon, ::::: eBC, : and attenuation measurements, b atn , were also performed with the AE33 multi-wavelengths aethalometer (model AE33, Magee Scientific, Aerosol d.o.o. Drinovec et al., 2015). The AE33 is based on the measurement at 7 different wavelengths (370,470,520,590,660,880, and 950 nm) of the transmission of light through two sample spots with different flows and particle loading relative to the reference spot. It derives the eBC concentration and the attenuation coefficients by applying eqs. (1) and (2), respectively, following Drinovec et al. (2015): where S is the filter surface area loaded with the sample, F 1 the volumetric flow of the spot 1, ζ the lateral airflow leakage, σ abs the mass-absorption cross-section, k the loading factor parameter and ∆ATN 1 the variation of attenuation of light of the filter tape loaded with the sample of the spot 1, ATN 1 , during the measurement timestamp ∆t.
Then, we determined the average and seasonal multiple scattering factor C both as the ratio between the AE33 attenuation coefficients and the absorption coefficients b λ abs :::::: b abs (λ) : measured by the MAAP and the PP_UniMI (eq. 5), and also by applying a Deming regression between the AE33 attenuation coefficients and the MAAP absorption coefficients for the :::::: overall 245 average values for each filter tape.
This value of the multiple scattering parameter C λ :::: C(λ) : is the value derived from the experimental comparison of different instruments, contrasting the default instrumental constant value C instr :: C 0 . The data availability at BCN station ranged between 250 periods at the three stations as shown in Fig. S1.

Aerosol scattering measurements
On-line particle total scattering (b sp ) and hemispheric backscatter (b bsp ) coefficients were measured on-line at the three sites with LED-based integrating nephelometers (Aurora 3000, ECOTECH Pty , Ltd, Knoxfield, Australia) operating at three wavelengths (450, 525 and 635 nm). Calibration of the nephelometers was performed three times per year using CO 2 as span gas 255 while zero adjusts were performed once per day using internally filtered particle-free air. The RH threshold was set by using a processor-controlled automatic heater inside the Aurora 3000 nephelometer to ensure a sampling RH of less than 40 % (GAW, 2016). σ sp coefficients were corrected for non-ideal illumination of the light source and for truncation of the sensing volumes following the procedure described in Müller et al. (2011b).

Data treatment and conceptual model 260
The different analyses performed herein were performed considering the absorption coefficients provided either by the MAAP or the PP_UniMI as reference absorption measurements depending on either time resolution and coverage, or on the measurement availability at several wavelengths. The AE33 and MAAP data (provided with 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 low temporal resolution but at different wavelengths) were used to determine the wavelength dependence of the C factor. As aforementioned, the seasonal analysis of the C factor, its average values and the study of its cross-sensitivity to scattering were performed using the long high-time resolution dataset from the MAAP and AE33 measurements at the three measurement sites. For this, we applied eq. (5) using the absorption coefficient from the MAAP and the AE33 attenuation coefficient extrapolated to the 637 nm wavelength of the MAAP through the Ångström exponent obtained from the AE33 measurements 270 at 7 wavelengths.
The cross-sensitivity to scattering which, as shown later, can strongly affect the C factor values, is neglected in AE33 applications where it is generally assumed that the measured light attenuation is only due to the absorption of light by the collected particles (eqs. 1-2). Moreover, it is also generally assumed that the multiple scattering by particles is sample independent, or constant, and can be taken into account by introducing the multiple scattering correction factor C (Drinovec et al., 2015).

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However, this assumption is a first approximation, since the attenuation of transmitted light is also due to the scattering of light by the collected particles (Bond et al., 1999;Arnott et al., 2005). Taking this dependence into account and following Arnott et al. (2005) , Schmid et al. (2006) and Segura et al. (2014), we parameterized the light attenuation coefficient as : to obtain the relationship between the absorption, attenuation and scattering coefficients : where f (AT N ) is the function which contains all the dependencies of the measurement shown in eq. (4), i.e. filter loading correction and leakage, and can be assumed to be close 1 (Schmid et al., 2006).

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The absorption coefficients from the PP_UniMI were inter/extrapolated to the seven AE33 wavelengths using the absorption ::::::::: attenuation Ångström exponent : , ::::::: obtained ::::::: through : a :::::: log-log ::: fit from the PP_UniMI absorption measurements. MAAP and PP_UniMI using for the PP_UniMI data inversion the same assumptions as those performed in the MAAP (PaM approach) and reported a 1:1 correlation between the two instruments. Given that most of the aethalometer C values reported in literature were obtained by comparing AE33 attenuation measurements and MAAP absorption measurements, we report here also the median C values obtained comparing the AE33 with the PP_UniMI (Table S2) and with PaM (Table S3).
Density distribution of the C factor for each filter type, TFE-coated glass (also known as M8020) and M8060, at BCN, MSY, 420 and MSA station. The vertical line represents the median value of each distribution.
Wavelength dependence of C at a) MSY and, b) MSA comparing b atn from the AE33 measured at each wavelength and b abs inter/extrapolated to the same wavelength from the PP_UniMI. Box plots have been obtained as in Fig. 3 and separated into 540 two categories depending whether Saharan dust outbreaks took place (dust) or not (no-dust).

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Saharan dust outbreaks) as demonstrated by the negative Ångström exponent of the SSA (SSAAE) at high SSA. Thus, in prior studies, negative values of the SSAAE have been associated with an aerosol mixture dominated by mineral dust (Collaud Coen et al., 2004;Ealo et al., 2016;Yus-Díez et al., 2020). Moreover, we have found AAE values higher than 1.5 above a SSA of 0.95 (Fig. S6), thus implying a relatively higher absorption fraction in the UV range whether by dust absorbing particles or by BrC aerosols (Kirchstetter et al., 2004b;Chen and Bond, 2010;Zotter et al., 2017;Forello et al., 2019Forello et al., , 2020.
Code and data availability. The Montseny and Montsec data sets used for this publication are accessible online on the WDCA (World Data Centre for Aerosols) web page: http://ebas.nilu.no. The Barcelona data sets were collected within different national and regional projects and/or agreements and are available upon request. The code used for analysis can be obtained upon request to the corresponding author.
Author contributions. DC, SV, RV and VB performed and analyzed the measurements with the PP_UniMI polar photometer. NP, CR, MP, AA and JYD carried out the maintenance and supervision of the BCN, MSY and MSA supersites. AA, GM, MP and XQ played a crucial role in the processes of shaping the manuscript structure as well as helping with the data analysis. JYD developed the data process, the analysis of the results, and summarized and expressed them in this manuscript. All authors provided advice regarding the manuscript structure and 795 content as well as contributed to the writing of the final manuscript.
Competing interests. At the time of the research, MR and MI were also employed by the manufacturer of the Aethalometer AE33.
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