The Multi-Wavelength Absorption Analyzer ( MWAA ) Model as a Tool for Source and Component Apportionment Based on Aerosol Absorption Properties : Application to Samples Collected in Different Environments

The multi-wavelength absorption analyzer model (MWAA model) was recently proposed to provide a source (fossil fuel combustion vs. wood burning) and a component (black carbon BC vs. brown carbon BrC) apportionment of babs measured at different wavelengths, and to provide the BrC Ångström Absorption exponent (αBrC). This paper shows MWAA model performances and issues when applied to samples impacted by different sources. To this aim, the MWAA model was run on samples collected at a rural (Propata) and an urban (Milan) site in Italy during the winter period. Lower uncertainties on αBrC and a better correlation of the BrC absorption coefficient (babs) with levoglucosan (tracer for wood burning) were obtained in Propata (compared to Milan). Nevertheless, the correlation previously mentioned improved, especially in Milan, when providing a priori information on αBrC to MWAA. Possible reasons for this improvement could be the more complex mixture of sources present in Milan and the aging processes, which can affect aerosol composition, particle mixing, and size distribution. OC and EC source apportionment showed that wood burning was the dominating contributor to the carbonaceous fractions in Propata, whereas a more complex situation was detected in Milan. Simultaneous babs(BC) apportionment and EC measurements allowed MAC determination, which gave analogous results at the two sites.


Introduction
Scattering and absorption properties of atmospheric aerosol are directly responsible for aerosol-radiation interactions.In particular, aerosol light absorption provides a positive contribution to the Earth radiation balance.In addition to the aerosol-radiation effects, absorbing aerosol immersed in cloud droplets absorbs light and facilitates water evaporation and cloud dispersion, an additional indirect effect that counteracts the cooling effect of cloud droplet nucleation [1].Among absorbing species, the black carbon (BC) is the main global-warming contributor in atmospheric aerosol.Nevertheless, great uncertainties (about 1 order of magnitude) are still associated with the estimates of its radiative forcing contribution.They are mainly related to difficulties in assessing BC spatial-temporal distribution and in the evaluation of the effects of the mixing state on BC optical properties [1,2].
Pure BC is assumed to have an imaginary part of the refractive index independent of the wavelength (λ).Thus, for pure BC small spheres the expected λ-dependence of the BC absorption coefficient is b abs BC (λ)~λ −1 (e.g., [3]).In the past, BC and mineral dust were considered as the only light-absorbing components in the atmospheric aerosol.In the last decade, another aerosol component-the brown carbon (BrC) [4]-has been evidenced as a further contributor to absorption.BrC is composed of organic material that weakly absorbs radiation at long visible wavelengths but with enhanced absorption behavior towards short wavelengths.Its absorption characteristics can, in principle, provide a positive contribution to the Earth radiation balance both as pure material and modifying BC absorption characteristics by mixing effects (see e.g., [5,6]), but the extent of these effects is still under debate [7,8].Indeed, inconsistencies between theoretical/laboratory tests and in-field observations were reported ( [9] and therein cited literature).For this reason, most climate modeling approaches currently do not include possible effects related to BC and BrC mixing [9,10].BrC is still poorly characterized due to its chemical complexity (affecting also optical properties) and unclear emission sources and formation processes.Compounds contributing to BrC were reported to span from extremely low volatility compounds (ELVOC)-e.g., Humic-Like Substances (HULIS)-to much more volatile compounds related to secondary organic aerosol (SOA) ( [9] and therein-cited literature), even if the contribution to absorption seems to be dominated by ELVOC [11,12].Also, BrC source emissions merit further investigation: wood burning has been identified as an important primary BrC source (e.g., [11,[13][14][15]).Recently, other possible sources of BrC have been reported, e.g., biogenic contributions, BrC formation due to secondary processes [9], and possible BrC emissions by gasoline vehicles [16] or coal combustion [17].Nevertheless, BrC sources other than wood burning are generally neglected in optical source apportionment approaches (e.g., [18][19][20][21]).Also BrC light-absorption properties need further investigation.Indeed, the chemical complexity of BrC affects its optical behavior.For example, an increase of light absorption potential at increasing molecular weight was reported [12,22].Furthermore, the combustion efficiency and photochemical or aging processes affect BrC optical properties [23].Despite all these issues, attempts of including BrC in climate models are developing in recent years ( [24] and therein-cited literature).
It is noteworthy that several studies on BrC absorption properties and mass absorption coefficient were carried out after BrC extraction in water or solvents (see e.g., [15,[25][26][27][28][29][30][31]).Nevertheless, particle optical properties-even for homogeneous particles-depend on particle size and shape in the atmosphere (see e.g., [32]), which can be different from the properties of bulk or extracted material.To provide more robust information on the properties of BrC-containing particles, studies carried out on bulk/extracted material can be coupled to optical models (e.g., by Mie theory or the core-shell model), but also in this case assumptions, e.g., on particle size and mixing state, are needed (see, e.g., [31]).Thus, it is important to carry out studies aimed at providing information on BrC absorption characteristics minimizing the sample pre-treatment.
Moving in the previous frame, source apportionment models based on multi-λ measurements of the aerosol absorption coefficient (b abs (λ)), determined on aerosol collected on filter with no further treatments, were proposed in the literature (i.e., the Aethalometer model [18] and the Multi-Wavelength Absorption Analyzer model (MWAA model) [20]).The Aethalometer model is a widespread model providing information on source contributions by fossil fuel combustion (FF) and wood burning (WB).It is based on assumptions about the Ångström absorption exponent (α) of the two sources.As a step forward, Massabò et al. [20] proposed the MWAA model to provide not only a source (FF and WB) but also a component (BC and BrC) apportionment of b abs (λ).Furthermore, the MWAA model can provide information on α for BrC (α BrC ).
Massabò et al. [20] applied the MWAA model to multi-λ b abs (λ) data measured off-line by laboratory instrumentation (Multi-Wavelength Absorption Analyzer [20,33]).Nevertheless, the model can be applied to any b abs (λ) data, provided that at least 4-λ measurements are performed.For example, off-line measurements performed by the polar photometer PP_UniMI [34,35] or on-line Aethalometer measurements (properly corrected) [36] can be other possible inputs to the MWAA model.The b abs (λ) measurements carried out by such instruments do not require any sample treatment after particle collection.Thus, it is expected that the α BrC information provided by the MWAA model on such data represents the BrC optical absorption behavior in atmosphere better than measurements carried out after BrC water/solvent extraction -even if re-arrangement of BrC material on filter fibers cannot be excluded [37].
In this work, a comparison is performed between the MWAA model performances on PM10 (i.e., particles with an aerodynamic diameter lower than 10 µm) datasets collected at sites with different characteristics.The first dataset was collected at a rural background site in the Italian Appennines.The second dataset was collected at an urban background site in Milan (Italy).In the paper, we evidence merits and issues of the application of the MWAA model at the two sites.

Sites and Sampling
The data reported in this manuscript are referred to two different campaigns.The first campaign was performed in Propata, a rural site in Italy.Propata is a small village (less than 150 inhabitants) at 990 m a.s.l. in the Ligurian Appennines.During wintertime, low temperatures are usually reached and wood burning is extensively used for domestic heating and cooking [20,33,38].PM10 samples were collected on pre-fired (700 • C, 1-h) quartz-fiber filters (47 mm diameter, 2500QAO-UP, Pall) using a low-volume sampler (flow-rate 2.3 m 3 /h, European inlet compliant with the EN-12341 norm).Sampling duration was 48-h from midnight to midnight.Aerosol sampling was performed between 7th November 2014 and 7th January 2015.Twenty-eight PM10 samples were available in total.
The second sampling campaign was performed in Milan (Italy) at an urban background site placed on the roof (about 10 m a.g.l.) of the Department of Physics of the University of Milan.Milan is situated in the Po Valley, which is one of the main hot-spot pollution areas in Europe.For this reason, different source apportionment studies by receptor models based on chemical characterization were carried out in the last decade on integrated aerosol size-fractions (e.g., [39][40][41][42]) and on suitably characterized [43] size-segregated samples [44].These works evidenced that the site is impacted by a complex mixture of sources; traffic (both exhaust and non-exhaust), wood burning, re-suspended dust, and industry were identified as the main primary sources, but secondary compounds play a key role in explaining the total measured mass.The influence of particle aging processes and the impact of both local and regional contributions were identified in the size-segregated study [44].PM10 samples were collected on pre-fired quartz fiber filters (same filter type and treatment as in Propata) using an EPA inlet operating at 1 m 3 /h.Twenty-eight samples with 12-h resolution (9-21 or 21-9) were collected in the period 21 November-21 December 2016.
The MWAA and PP_UniMI instruments measure the total light transmitted and diffused in the front and back hemispheres by blank and loaded filters.To obtain b abs (λ) from these measurements, multiple scattering between the layer containing the aerosol and the filter has to be properly considered.
To this aim, the radiative transfer model proposed by Hänel [45,46] for polycarbonate filters and extended by Petzold and Schönlinner [47] to fiber filters was applied.Briefly, the model inputs are the total light scattered in the front and back hemispheres by blank and loaded filters.The sample is modelled into two layers, one containing aerosol (aerosol-filter layer) and the other composed by the filter matrix only.All interactions between the aerosol-filter layer and the filter matrix are considered.The model outputs are the single scattering albedo (ω) and the optical depth (τ) of the aerosol-filter layer.As the absorption contribution is related to aerosol only, the absorbance (ABS) of the deposited aerosol can be evaluated as ABS = (1 − ω)•τ.Sampling volume (V) and deposit area (A) can be then exploited to retrieve the aerosol absorption coefficient in air.It is noteworthy that-opposite to instrumentation based on transmitted light only-the simultaneous measurements of transmitted and scattered light avoid the need for correction algorithms to account for the scattering properties of the aerosol and/or of parallel measurements of the scattering coefficient.
The MWAA instrument and PP_UniMI differ in their ways of assessing the total light scattered in the front and back hemispheres.Indeed, the MWAA instrument applies the same approach presented in Petzold and Schönlinner [47]: information on light diffused at fixed angles is used-together with assumptions on the shape of the phase function for aerosol collected on fiber filters-to provide the total scattered light by analytical functions.On the contrary, PP_UniMI performs angular-resolved measurements with about 0.4 • resolution in the range 0-173 • .Then, the total amounts of the light diffused in the forward and back hemispheres are evaluated by solid angle integration.This allows PP_UniMI to operate also on aerosol collected on other filter matrices (e.g., membrane filters, see [35]) with no need for external information on the phase function shape.Assumptions on the phase function shape are needed only for extrapolating values in the range 173-180 • .
The Milan dataset was analyzed both by the MWAA instrument and PP_UniMI for sake of comparison.Scatterplots of MWAA and PP_UniMI measurements at comparable wavelengths (i.e., 635 nm, 532 nm, and 407/405 nm) are reported in Figure 1.Deming regression was performed as measurement uncertainties are comparable between the two instruments (about 10%).It is noteworthy that all regression line slopes were compatible to 1 and intercepts were compatible to 0 for significant level of 0.02.Furthermore, measurements were very well correlated with correlation coefficient R > 0.98 at all wavelengths.
Atmosphere 2017, 8, 218 4 of 18 (τ) of the aerosol-filter layer.As the absorption contribution is related to aerosol only, the absorbance (ABS) of the deposited aerosol can be evaluated as ABS = (1 − ω)⋅τ.Sampling volume (V) and deposit area (A) can be then exploited to retrieve the aerosol absorption coefficient in air.It is noteworthy that-opposite to instrumentation based on transmitted light only-the simultaneous measurements of transmitted and scattered light avoid the need for correction algorithms to account for the scattering properties of the aerosol and/or of parallel measurements of the scattering coefficient.
The MWAA instrument and PP_UniMI differ in their ways of assessing the total light scattered in the front and back hemispheres.Indeed, the MWAA instrument applies the same approach presented in Petzold and Schönlinner [47]: information on light diffused at fixed angles is usedtogether with assumptions on the shape of the phase function for aerosol collected on fiber filtersto provide the total scattered light by analytical functions.On the contrary, PP_UniMI performs angular-resolved measurements with about 0.4° resolution in the range 0-173°.Then, the total amounts of the light diffused in the forward and back hemispheres are evaluated by solid angle integration.This allows PP_UniMI to operate also on aerosol collected on other filter matrices (e.g., membrane filters, see [35]) with no need for external information on the phase function shape.Assumptions on the phase function shape are needed only for extrapolating values in the range 173-180°.
The Milan dataset was analyzed both by the MWAA instrument and PP_UniMI for sake of comparison.Scatterplots of MWAA and PP_UniMI measurements at comparable wavelengths (i.e., 635 nm, 532 nm, and 407/405 nm) are reported in Figure 1.Deming regression was performed as measurement uncertainties are comparable between the two instruments (about 10%).It is noteworthy that all regression line slopes were compatible to 1 and intercepts were compatible to 0 for significant level of 0.02.Furthermore, measurements were very well correlated with correlation coefficient R > 0.98 at all wavelengths.

Chemical Characterization
After being analyzed with the MWAA instrument (and PP_UniMI in the case of Milan samples only), one punch (1.5 cm 2 ) of each filter was extracted by sonication (1-h) using 5 mL ultrapure (Milli-Q) water.The extract was analyzed to determine levoglucosan concentration by High-Performance Anion Liquid Chromatography coupled with Pulsed Amperometric Detection (HPAEC-PAD) following the procedure described in [48].Minimum detection limit is about 2 ng/mL (i.e., 0.7 ng/m 3 in Propata and 6.6 ng/m 3 in Milan, due to different sampling conditions) and uncertainties are about 11%.
For the determination of the carbonaceous fraction, a second filter punch (1.0 cm 2 ) of each filter

Chemical Characterization
After being analyzed with the MWAA instrument (and PP_UniMI in the case of Milan samples only), one punch (1.5 cm 2 ) of each filter was extracted by sonication (1-h) using 5 mL ultrapure (Milli-Q) water.The extract was analyzed to determine levoglucosan concentration by High-Performance Anion Liquid Chromatography coupled with Pulsed Amperometric Detection (HPAEC-PAD) following the procedure described in [48].Minimum detection limit is about 2 ng/mL (i.e., 0.7 ng/m 3 in Propata and 6.6 ng/m 3 in Milan, due to different sampling conditions) and uncertainties are about 11%.
For the determination of the carbonaceous fraction, a second filter punch (1.0 cm 2 ) of each filter was analyzed by a Thermal Optical transmittance (TOT) instrument (Sunset Laboratory Inc.).Propata samples were analyzed following the EUSAAR_2 protocol [49], while a NIOSH-like protocol (He_870) [50] has been used in the case of the Milan samples.This choice has been taken to have continuity with previous respective measurement campaigns.Minimum detection limit is 0.15 µg carbon, corresponding to 0.02 µg/m 3 in Propata and 0.15 µg/m 3 in Milan due to different sampling conditions.Analytical uncertainties were about 10-15% depending on the carbon fraction.

Optical Source and Component Apportionment: The Multi-Wavelength Absorption Analyzer Model
In this work, the optical approach known as Multi-Wavelength Absorption Analyzer model (MWAA model) was applied to perform source and component apportionment of b abs (λ) and carbonaceous fractions (OC and EC).The detailed description of the model bases can be found elsewhere [20].In the following paragraphs, only the summary of the main steps necessary for the apportionment will be recalled.

Aerosol Absorption Coefficient Apportionment
The MWAA model requires b abs (λ) as input, at least at 4 λs.The final outputs are the b abs (λ) contributions due to BC by fossil fuel combustion, BC by wood burning, and BrC (i.e., b abs,FF BC (λ), b abs,WB BC (λ), and b abs BrC (λ), respectively), as well as information on α BrC .
The model starts from the following assumptions for component apportionment: according to expectancies for pure, small BC spheres (e.g., [3]) as often applied in the literature (e.g., [51]).Nevertheless, different choices can be in principle be performed due to the possible effect of BC core and coating sizes on the Ångström absorption exponent (e.g., [52]).
Under the previous assumptions, the total aerosol absorption coefficient can be represented as: Provided that data of b abs (λ) are available for at least 4 λs, the data can be fitted as a function of λ to determine A, B, and α BrC in Equation ( 1).The result of the fit directly allows calculating component-apportionment of b abs (λ) and provides information on α BrC , which is still rare in the literature for what concerns measurements on not pre-treated samples.Pokhrel et al.
[6] performed measurements by multi-λ photoacoustic devices on air sampled as-is and after passing through a thermo-denuder, and used different approaches to apportion the BrC contribution to the total b abs , but no indication of α BrC was explicitly reported.
Further insights can be obtained exploiting results of the Aethalometer model [18,19,53].The Aethalometer model provides b abs (λ) source apportionment under the following assumptions: (d) fossil fuels combustion (FF) and wood burning (WB) are the only aerosol sources producing light-absorbing aerosol; (e) for each source, the absorption coefficient is proportional to λ −α , where α is source-dependent; (f) α for fossil fuel combustion (α FF ) aerosol is assumed a priori to be the same as α BC -i.e., in this work α FF =1, as is often found in several works from the literature (e.g., [54][55][56]); (g) α for wood-burning aerosol (α WB ) is assumed a priori.
Under the previous assumptions, it holds: It is noteworthy that in the Aethalometer model b abs FF (λ) and b abs WB (λ) are obtained.Unlike the Aethalometer model which derives A' and B' starting from information at two λs only, with the MWAA model A' and B' are obtained by fitting b abs (λ) data at all available λs using Equation (2).
To perform source and component apportionment of b abs (λ), the MWAA model combines Equation (1) and Equation ( 2) under the following assumptions: (h) α FF = α BC , (i) BrC is emitted by wood burning only.
From these assumptions, once A, B, α BrC , A , and B are obtained by the two fit procedures, b abs,FF BC (λ), b abs,WB BC (λ), and b abs BrC (λ) can be derived as presented in Equation ( 3) (details for calculation can be found in Massabò et al. [20] and a sketch of the procedure is present in the supplemental material (1)): Among the several parameters needed for running the MWAA model, the choice of the value to be attributed to α WB is the most critical, since it depends, at least, on the kind of wood burnt and on meteorology.In the literature, values between 1.6 and 2 have been reported when performing optical source apportionment of ambient aerosol [18][19][20]33,57,58].For this reason, we decided to support our choice exploiting previous information available at each site.In a previous study in Propata, source apportionment was carried out both from 14 C and optical measurements.Input α WB for optical source apportionment was varied and α WB = 1.8 gave the best agreement with 14 C source apportionment results [20].Thus, α WB = 1.8 was used also in this work for the Propata dataset.In the case of Milan, performing the same choice led to an unreasonably high contribution from wood burning compared to previous studies based on 14 C measurements [41] or Positive Matrix Factorization on well chemically characterized samples [40,42].So, we finally chose α WB = 2 in Milan.

Determination of Equivalent Black Carbon Mass-Absorption Coefficient
Equivalent black carbon (EBC) in atmosphere is generally calculated from b abs measurements, assuming that b abs is due to black carbon absorption contribution only and using a suitable λ-dependent mass absorption coefficient MAC(λ).
The MAC of atmospheric EBC spans a relatively wide range of values in the literature (e.g., [2,54]) and it is recognized to be site-and season-dependent.Among the reasons for this variability, it is worth mentioning the different methodologies used for EBC determination [59] and the neglect of possible components of other BC contributing to b abs (λ) (e.g.mineral dust [60]), together with possible mixing effects (see e.g., [6,61]).As no direct measurement of BC mass is possible [59], the EC measured by thermal-optical transmittance method (par.2.3) was assumed as a proxy for EBC in this work.This allowed providing the EBC MAC (MAC EBC ) at different λs.Indeed, Equation ( 4) can be re-written as follows, exploiting b abs BC (λ) obtained by the MWAA model to determine MAC(λ) (Equation ( 5)): MAC EBC (λ) In principle, any wavelength can be chosen as reference for b abs BC and b abs,FF BC .Nevertheless, it is expected that lower uncertainty affects optical apportionment at long wavelengths, due to the lower contribution to the total b abs from BrC.Further detail on the methodology can be found in [20].

OC Source Apportionment
OC source apportionment is less straightforward.Indeed, non-absorbing OC by combustion sources and OC by non-combustion sources (OC NC ) can contribute to OC.The methodology used in the MWAA model for OC source apportionment stems from tracer approaches.These methods assume that a component emitted by the source can be clearly apportioned (the tracer) and that another is emitted with constant ratio with the tracer.In this way, the second component can be obtained by the tracer using a suitable emission ratio.The approach is widely used in the literature for OC source apportionment, e.g., based on 14 C measurements [41,62].The approach has already been extended in source apportionment studies based on optical properties, with further assumptions on proportionality between species and optical properties [18][19][20].
OC source apportionment by the MWAA model assumes that: (j) OC from fossil fuel combustion (OC FF ) is proportional to EC FF and-assuming that the MAC for BC has limited variability in the considered dataset-to b abs,FF BC .It is preferable to perform OC source apportionment starting from optical measurements to reduce uncertainty propagation; (k) OC from wood burning combustion (OC WB ) is proportional to BrC and-assuming that the MAC for BrC has limited variability in the considered dataset-to b abs BrC ; in this case, it is suggested to exploit information on b abs BrC at the shortest available wavelength to maximize the relative contribution of BrC to the total b abs .
Summarizing, as 5-λ measurements are available for both the considered datasets, OC source apportionment will be performed using Equation (7): Massabò et al. [20] proposed to determine k 1 on samples where little wood burning impact was expected, so that Equation (7) reduces to OC = k 1 •b abs BC (850 nm) + OC NC .Nevertheless, such approach is hardly applicable when only winter samples are available, especially at sites where high contribution due to wood burning for domestic heating is expected.So, in this work we propose to obtain k 1 and k 2 by multiple linear regression of OC vs. b abs BC (850 nm) and b abs BrC (375 nm), under the assumption that OC NC can be assumed nearly constant or provides a minor contribution to total OC.The main limitation of the method is related to possible difficulties in apportioning secondary OC.Nevertheless, k 1 and k 2 are derived by multiple linear regression of real-world measurements.
Real-world profiles have already been proven to have the potential to account for rapidly formed secondary compounds, thus limiting the problem of secondary OC apportionment only to secondary OC formed with great time-delay from precursor emissions (which can provide contribution to OC NC ) [44,63].

Results from the Propata Dataset
The 5-λ temporal trend of b abs measured in Propata using the MWAA instrument is shown in Figure 2, together with the apparent Ångström absorption coefficient (α exp , determined by fitting each set of 5-λ data by a λ −αexp function).It should be noted that α exp was in the range 1.31-1.85,providing a first indication of important contributions by sources other than fossils during the whole period.The MWAA model was run on the Propata dataset, as explained in par.2.4.In Figure 3, results obtained for αBrC and fit error are represented.It is noteworthy that in 79% cases, the fit error was lower than 3%.In these cases, very close αBrC values were found in different samples: αBrC = 3.79 ± 0.10 (i.e., 2.5% standard deviation) with a minimum-maximum range of 3.58-3.99.Assuming wood burning as the main source of BrC, we analyzed the correlation between babs BrC (λ) and levoglucosan (tracer for wood burning).It was noticed that the correlation decreased at increasing wavelengths (see as an example the scatterplots of babs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration shown in Figure 4a).Furthermore, the most scattered points were those showing high uncertainties for αBrC.
Two hypotheses were performed concerning these points: (a) The two-component model was not applicable.This can occur, e.g., in case of Saharan dust events when a non-negligible absorption contribution from dust can be, in principle, observed.The MWAA model was run on the Propata dataset, as explained in par.2.4.In Figure 3, results obtained for α BrC and fit error are represented.It is noteworthy that in 79% cases, the fit error was lower than 3%.In these cases, very close α BrC values were found in different samples: α BrC = 3.79 ± 0.10 (i.e., 2.5% standard deviation) with a minimum-maximum range of 3.58-3.99.The MWAA model was run on the Propata dataset, as explained in par.2.4.In Figure 3, results obtained for αBrC and fit error are represented.It is noteworthy that in 79% cases, the fit error was lower than 3%.In these cases, very close αBrC values were found in different samples: αBrC = 3.79 ± 0.10 (i.e., 2.5% standard deviation) with a minimum-maximum range of 3.58-3.99.Assuming wood burning as the main source of BrC, we analyzed the correlation between babs BrC (λ) and levoglucosan (tracer for wood burning).It was noticed that the correlation decreased at increasing wavelengths (see as an example the scatterplots of babs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration shown in Figure 4a).Furthermore, the most scattered points were those showing high uncertainties for αBrC.
Two hypotheses were performed concerning these points: (a) The two-component model was not applicable.This can occur, e.g., in case of Saharan dust events when a non-negligible absorption contribution from dust can be, in principle, observed.Assuming wood burning as the main source of BrC, we analyzed the correlation between b abs BrC (λ) and levoglucosan (tracer for wood burning).It was noticed that the correlation decreased at increasing wavelengths (see as an example the scatterplots of b abs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration shown in Figure 4a).Furthermore, the most scattered points were those showing high uncertainties for α BrC .Two hypotheses were performed concerning these points: (a) The two-component model was not applicable.This can occur, e.g., in case of Saharan dust events when a non-negligible absorption contribution from dust can be, in principle, observed.Furthermore, it should be recalled that BrC refers to a complex mixture of organic compounds still poorly characterized.It cannot be excluded that BrC of various origins (e.g., wood burning vs. photochemical contribution) can have different features.(b) Numerical tests showed that quality of the MWAA model fit is quite sensitive to input data, even for input data variations within uncertainties.Random combination of data uncertainties can lead to configurations in the 5-λ b abs measurements, badly affecting the fit: e.g., numerical tests performed by shifting (within uncertainties) towards higher values b abs at short-λ and towards lower values b abs at long-λ showed important variations in α BrC results and an increase in the associated uncertainties.
Trying to understand which of these hypotheses affected the points with high uncertainties on α BrC , the MWAA model was re-run in a different way: fit of Equation ( 1) was performed by fixing α BrC = 3.79.This value has been calculated by averaging the α BrC values, considering only samples where the relative uncertainty was lower than 3%.This approach will henceforth be named "MWAA model with fixed α BrC ".The results obtained in this case for b abs BrC (λ) at 375 nm and 850 nm vs.
levoglucosan concentration are reported in Figure 4b.It is noteworthy that correlation at 850 nm strongly improved (R 2 = 0.96).This suggested that numerical instability was responsible for the few samples with α BrC affected by high uncertainties in Figure 3. Indeed, if a third absorbing component independent of wood burning was present in the dataset, no improving correlation with levoglucosan could be expected, even when imposing a α BrC characteristic for wood burning at the sampling site.
Atmosphere 2017, 8, 218 9 of 18 Trying to understand which of these hypotheses affected the points with high uncertainties on αBrC, the MWAA model was re-run in a different way: fit of Equation ( 1) was performed by fixing αBrC = 3.79.This value has been calculated by averaging the αBrC values, considering only samples where the relative uncertainty was lower than 3%.This approach will henceforth be named "MWAA model with fixed αBrC".The results obtained in this case for babs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration are reported in Figure 4b.It is noteworthy that correlation at 850 nm strongly improved (R 2 = 0.96).This suggested that numerical instability was responsible for the few samples with αBrC affected by high uncertainties in Figure 3. Indeed, if a third absorbing component independent of wood burning was present in the dataset, no improving correlation with levoglucosan could be expected, even when imposing a αBrC characteristic for wood burning at the sampling site.Total carbon (TC) absolute concentration in the Propata dataset was 1.7 ± 0.7 μg/m 3 (average ± standard deviation).OC represented, on average, 82% of TC, the remaining 18% being EC.Levoglucosan average concentration in Propata was 0.3 ± 0.2 μg/m 3 .
EC source apportionment was performed as explained in par.2.4.3, starting from b abs source apportionment obtained by the MWAA model with fixed α BrC .The relative contribution of EC FF (Equation ( 6)) to EC in Propata was 37% ± 22% (average ± standard deviation).Very good correlation was found between EC WB and levoglucosan (R 2 = 0.90, see Figure 5).The average levoglucosan/EC WB ratio in these samples was 1.6 ± 0.4.It is within the range obtained combining information on levoglucosan/OC and EC/OC ratios for wood burning emissions reported in [62] and the literature therein (0.9 ± 0.6).
EC source apportionment was performed as explained in par.2.4.3, starting from babs source apportionment obtained by the MWAA model with fixed αBrC.The relative contribution of ECFF (Equation 6) to EC in Propata was 37% ± 22% (average ± standard deviation).Very good correlation was found between ECWB and levoglucosan (R 2 = 0.90, see Figure 5).The average levoglucosan/ECWB ratio in these samples was 1.6 ± 0.4.It is within the range obtained combining information on levoglucosan/OC and EC/OC ratios for wood burning emissions reported in [62] and the literature therein (0.9 ± 0.6).Multiple linear regression was carried out for OC source apportionment as explained in par.2.4.4.Regression parameters were k1 = 0.24 ± 0.06, k2 = 0.35 ± 0.02, and OCNC = 0.30 ± 0.08, in which uncertainties represent the standard error of the regression.Scatterplot of reconstructed vs. measured OC concentration resulted into OCrec = 0.98⋅OCmeas, with R 2 = 0.89.OC in Propata was dominated by OCWB (63% ± 16%) and the contribution from fossil fuel combustion was much lower (13% ± 10%).Non-negligible contribution resulting from OCNC was present (25% ± 9%), and it is expected to be related to secondary and/or natural contributions.OCFF/ECFF ratio was 1.4 ± 0.3, which is in agreement with, e.g., real-world profiles for the traffic source obtained by PMF in Milan [40].OCWB/ECWB ratio in Propata was 5.0 ± 1.2.This ratio is within the range reported for primary wood burning emissions Multiple linear regression was carried out for OC source apportionment as explained in Section 2.4.4.Regression parameters were k 1 = 0.24 ± 0.06, k 2 = 0.35 ± 0.02, and OC NC = 0.30 ± 0.08, in which uncertainties represent the standard error of the regression.Scatterplot of reconstructed vs. measured OC concentration resulted into OC rec = 0.98•OC meas , with R 2 = 0.89.OC in Propata was dominated by OC WB (63% ± 16%) and the contribution from fossil fuel combustion was much lower (13% ± 10%).Non-negligible contribution resulting from OC NC was present (25% ± 9%), and it is expected to be related to secondary and/or natural contributions.OC FF /EC FF ratio was 1.4 ± 0.3, which is in agreement with, e.g., real-world profiles for the traffic source obtained by PMF in Milan [40].OC WB /EC WB ratio in Propata was 5.0 ± 1.2.This ratio is within the range reported for primary wood burning emissions (EC WB /OC WB = 0.16 ± 0.05 was reported in [62] and therein-cited literature, i.e., OC WB /EC WB = 6.3 ± 2.0).Nevertheless, it should be noticed that literature ratios were obtained from OC and EC measurements carried out with different thermal protocols, whose influence on the measurements will be better discussed in par.4.

Results from the Milan Dataset
Multi-λ b abs measurements on the Milan dataset were performed both using PP_UniMI and MWAA.As shown in par.2.2, measurements agreed very well between the instruments.In this paragraph, data obtained by the MWAA instrument will be presented throughout the text as they were performed at 5-λs (compared to 4-λ measurements performed by PP_UniMI).This improves the quality of the fits to be performed, as presented in par.2.4.1 due to a higher number of points.
Figure 6 represents the 5-λ temporal trend of b abs and α exp for the Milan dataset.In this dataset 1.19 ≤ α exp ≤ 1.69: values were lower than in Propata, providing a first indication of a higher relative contribution from fossil fuel combustion.

Results from the Milan Dataset
Multi-λ babs measurements on the Milan dataset were performed both using PP_UniMI and MWAA.As shown in par.2.2, measurements agreed very well between the instruments.In this paragraph, data obtained by the MWAA instrument will be presented throughout the text as they were performed at 5-λs (compared to 4-λ measurements performed by PP_UniMI).This improves the quality of the fits to be performed, as presented in par.2.4.1 due to a higher number of points.
Figure 6 represents the 5-λ temporal trend of babs and αexp for the Milan dataset.In this dataset 1.19 ≤ αexp ≤ 1.69: values were lower than in Propata, providing a first indication of a higher relative contribution from fossil fuel combustion.As already shown for Propata, Figure 7 represents αBrC and uncertainties obtained by the MWAA model.For the Milan dataset, αBrC uncertainty provided by the fit is lower than 3% only in 41% of the samples (in 75% cases it was lower than 10%).Nevertheless, as already found in Propata, stable values for αBrC were obtained when uncertainty was < 3%: αBrC = 3.81 ± 0.11 (i.e., 3% relative standard deviation) with a minimum-maximum range of 3.72-4.14.These values of αBrC are fully comparable to those obtained in Propata within variability (see Table 1).As already shown for Propata, Figure 7 represents α BrC and uncertainties obtained by the MWAA model.For the Milan dataset, α BrC uncertainty provided by the fit is lower than 3% only in 41% of the samples (in 75% cases it was lower than 10%).Nevertheless, as already found in Propata, stable values for α BrC were obtained when uncertainty was < 3%: α BrC = 3.81 ± 0.11 (i.e., 3% relative standard deviation) with a minimum-maximum range of 3.72-4.14.These values of α BrC are fully comparable to those obtained in Propata within variability (see Table 1).As already shown for Propata, Figure 7 represents αBrC and uncertainties obtained by the MWAA model.For the Milan dataset, αBrC uncertainty provided by the fit is lower than 3% only in 41% of the samples (in 75% cases it was lower than 10%).Nevertheless, as already found in Propata, stable values for αBrC were obtained when uncertainty was < 3%: αBrC = 3.81 ± 0.11 (i.e., 3% relative standard deviation) with a minimum-maximum range of 3.72-4.14.These values of αBrC are fully comparable to those obtained in Propata within variability (see Table 1).In Figure 8a, the scatterplot of b abs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration is reported.It is noteworthy that data were more scattered than for Propata dataset (Figure 4a): R 2 = 0.71 was found considering b abs (375 nm), whereas no trend line was inserted considering b abs (850nm) as no correlation is found.As already performed for Propata, the MWAA model with fixed α BrC was re-run also for the Milan dataset.In this test, α BrC = 3.81 was chosen, as it is the value obtained for the Milan dataset in the case of good fit of the original data.It can be noticed (Figure 8b) that also in this case the correlation between b abs BrC and levoglucosan improves in all cases (R 2 = 0.93).
Atmosphere 2017, 8, 218 11 of 18 In Figure 8a, the scatterplot of babs BrC (λ) at 375 nm and 850 nm vs. levoglucosan concentration is reported.It is noteworthy that data were more scattered than for Propata dataset (Figure 4a): R 2 = 0.71 was found considering babs(375 nm), whereas no trend line was inserted considering babs(850nm) as no correlation is found.As already performed for Propata, the MWAA model with fixed αBrC was rerun also for the Milan dataset.In this test, αBrC = 3.81 was chosen, as it is the value obtained for the Milan dataset in the case of good fit of the original data.It can be noticed (Figure 8b) that also in this case the correlation between babs BrC and levoglucosan improves in all cases (R 2 = 0.93).TC average concentration in Milan was 13 ± 5 μg/m 3 .On average, 84% of TC was OC, with the remainder being EC.Levoglucosan average concentration in Milan was 0.7 ± 0.3 μg/m 3 .
Also for the Milan dataset, data obtained by running the MWAA model with fixed αBrC were used for EC and OC apportionment.From optical apportionment (Equation ( 6)), EC resulted mainly of fossil origin in most cases (range 62-87%, except three cases in the range 42-44%), consistent with 14 C studies in the Milan area [40] and in other cities in Europe during wintertime [62,64].As already TC average concentration in Milan was 13 ± 5 µg/m 3 .On average, 84% of TC was OC, with the remainder being EC.Levoglucosan average concentration in Milan was 0.7 ± 0.3 µg/m 3 .
Also for the Milan dataset, data obtained by running the MWAA model with fixed α BrC were used for EC and OC apportionment.From optical apportionment (Equation ( 6)), EC resulted mainly of fossil origin in most cases (range 62-87%, except three cases in the range 42-44%), consistent with 14 C studies in the Milan area [40] and in other cities in Europe during wintertime [62,64].As already found between b abs BrC and levoglucosan, very good correlation was found also between b abs,WB BC and levoglucosan (R 2 = 0.92).Nevertheless, only discrete correlation was found between EC WB and levoglucosan (R 2 = 0.56).It should be evidenced that the initial correlation between b abs (850 nm) and EC is lower than in Propata (R 2 = 0.83 in Milan vs. R 2 = 0.94 in Propata), and this can affect the apportionment of absolute EC concentrations.Furthermore, it should be noticed that in four samples ABS values higher than 0.90 were found.In these cases, shadowing effects (e.g., [36]) can occur leading to an underestimation of the measured b abs , thus increasing measurement uncertainty and possibly impacting also the source apportionment model.By removing these points, the correlation rises to R 2 = 0.70 (Figure 9).The average levoglucosan/EC WB ratio in these samples was 1.3 ± 0.5, which is fully comparable with the value obtained combining information on levoglucosan/OC and EC/OC ratios for wood-burning emissions reported in [62] and therein-cited literature (0.9 ± 0.6).Furthermore, the value is fully comparable to the one obtained in Propata within variabilities (see Table 2).
Atmosphere 2017, 8, 218 12 of 18 ratios for wood-burning emissions reported in [62] and therein-cited literature (0.9 ± 0.6).Furthermore, the value is fully comparable to the one obtained in Propata within variabilities (see Table 2).Multiple linear regression for OC source apportionment (par.2.4.4.) on Milan dataset resulted in k1 = 0.33 ± 0.05, k2 = 0.34 ± 0.07, and OCNC =1.1 ± 1.0, where uncertainties are the standard error of the regression.It is noteworthy that OCNC is comparable to zero within 2 standard errors.Reconstructed vs. measured OC concentration resulted into OCrec = 0.98⋅OCmeas, with R 2 = 0.82.Moreover, about ± 20% difference between measured and reconstructed concentration was registered, except in two samples.These samples were the same providing the two lowest values for αBrC (Figure 7).This suggests that these samples are impacted by different sources/processes modifying the optical characteristics compared to the others (e.g., [52]); for this reason, they will be excluded by the following statistics.As far as OCFF, OCWB, and OCNC are concerned, they contributed 40% ± 14%, 48% ± 14%, and 12% ± 4% to the OC, respectively (average ± standard deviation).OCFF/ECFF average ratio was 3.0 ± 0.7.This value was higher than the ratio expected for primary emission (e.g., [65] and therein-cited literature), but it was compatible to the average OCFF/ECFF previously found in Milan from 14 C measurements (2.3 ± 0.8) within variability [41].OCWB/ECWB average ratio was 10 ± 3. Also, in this case, this ratio is higher than what reported for primary wood burning emissions (ECWB/OCWB = 0.16 ± 0.05 was reported in [62], i.e., OCWB/ECWB = 6.3 ± 2.0).Nevertheless, literature works suggest that secondary contribution from wood burning comparable to the primary one can be expected [66,67].Thus, the approach seems able to associate at least part of the secondary compounds rapidly formed in atmosphere to specific sources.This ability of receptor models has already been evidenced in other source apportionment studies based on chemical aerosol properties carried out in the area [44,63].Multiple linear regression for OC source apportionment (Section 2.4.4) on Milan dataset resulted in k 1 = 0.33 ± 0.05, k 2 = 0.34 ± 0.07, and OC NC =1.1 ± 1.0, where uncertainties are the standard error of the regression.It is noteworthy that OC NC is comparable to zero within 2 standard errors.Reconstructed vs. measured OC concentration resulted into OC rec = 0.98•OC meas , with R 2 = 0.82.Moreover, about ± 20% difference between measured and reconstructed concentration was registered, except in two samples.These samples were the same providing the two lowest values for α BrC (Figure 7).This suggests that these samples are impacted by different sources/processes modifying the optical characteristics compared to the others (e.g., [52]); for this reason, they will be excluded by the following statistics.As far as OC FF , OC WB , and OC NC are concerned, they contributed 40% ± 14%, 48% ± 14%, and 12% ± 4% to the OC, respectively (average ± standard deviation).OC FF /EC FF average ratio was 3.0 ± 0.7.This value was higher than the ratio expected for primary emission (e.g., [65] and therein-cited literature), but it was compatible to the average OC FF /EC FF previously found in Milan from 14 C measurements (2.3 ± 0.8) within variability [41].OC WB /EC WB average ratio was 10 ± 3. Also, in this case, this ratio is higher than what reported for primary wood burning emissions (EC WB /OC WB = 0.16 ± 0.05 was reported in [62], i.e., OC WB /EC WB = 6.3 ± 2.0).Nevertheless, literature works suggest that secondary contribution from wood burning comparable to the primary one can be expected [66,67].Thus, the approach seems able to associate at least part of the secondary compounds rapidly formed in atmosphere to specific sources.This ability of receptor models has already been evidenced in other source apportionment studies based on chemical aerosol properties carried out in the area [44,63].

Discussion
By comparing the results obtained in the two datasets, two features appeared: (a) The MWAA model provided more robust measurements of α BrC on single samples in the Propata dataset (in 79% vs. 41% of the cases the fit uncertainty associated with α BrC is lower than 3%).(b) More samples with high uncertainty associated to α BrC lead to a lower correlation between b abs BrC and levoglucosan concentration in Milan.
In principle, the latter observation can be related to site-specific characteristics (e.g.source mixture or particle aging), to numeric instability, or both.The results of the test performed by fixing α BrC at each site to the average value for α BrC low-uncertainty samples showed that correlation between b abs BrC and levoglucosan improved.This provided an indication that wood burning (traced by levoglucosan) dominated BrC concentration at both sites.Indeed, if contributions from other sources emitting important absorbers or BrC species with strongly different optical properties were present in the samples, a weaker correlation with a marker from a specific source would have been found.
Nevertheless, it can be noticed that b abs BrC vs. levoglucosan correlation is slightly worse in Milan (R 2 = 0.93) than in Propata (R 2 = 0.96).Possible reasons could be the more complex mixture of sources present in Milan and the aging processes [40,42,44], which can affect aerosol composition, particle mixing, and size distribution.Small variations in BrC properties related to these factors could have influenced the MWAA model results, leading to a higher percent of cases in which α BrC was affected by high uncertainties.
Absolute TC average concentrations at the two sites were 7.7 times higher in Milan than in Propata.This is consistent with the peculiarities of the sites: Milan is placed in the Po Valley, which is one of the main hot-spot pollution areas, and it is often affected by strong stability conditions during wintertime [68,69]; Propata is a small village in the Appennines; very few local sources are present in Propata and it is only occasionally impacted by transports from the Po Valley.The high wood-burning contributions of EC and OC in Propata are easily explained by the wide use of wood burning for domestic heating at the site.Even if the relative contribution of OC and EC to TC seems to be comparable at the two sites, it should be recalled (par.2.3) that carbonaceous fractions were measured by the EUSAAR_2 protocol in Propata and by a NIOSH-like protocol (He_870) in Milan.In a previous study [50], it was shown that the ratio of EC measured with the two protocols was EC EUSAAR_2 /EC He_870 = 1.49 for winter samples collected in Milan.Thus, relative EC contribution to TC reported to the same thermal protocol is about 1.5 times higher in Milan than in Propata.The use of different thermal protocols and their effect on EC quantification impacted also on apparent MAC (Equation ( 5)) measured at the sites: the MAC was 6.3 ± 1.1 m 2 /g and 9.1 ± 1.9 m 2 /g at 850 nm in Propata and Milan, respectively.If the influence of the thermal protocol on EC quantification is considered, the MAC values determined at the two sites are fully comparable within variabilities and they are in the range of results recently reported in the literature in the European boundary layer [70].
It is very interesting to note that both the constant k 1 relating b abs BC (850 nm) to OC FF and k 2 relating b abs BrC (375 nm) to OC WB were compatible within uncertainties between the sites (see Table 1).
Nevertheless, OC/EC ratios were much higher in Milan than in Propata for both fossil fuel combustion and wood burning contributions, especially considering the differences in EC and OC quantification related to the thermal protocol (see Table 2).This can be related to the peculiarity of the Milan site: stagnation conditions may foster aging processes, increasing the OC/EC ratio [65].As the ability of receptor models to relate rapidly-formed secondary compounds to the primary emitted species has been proven in the literature [44,63], rapidly-formed secondary compounds in Milan can be associated to primary emissions by the model.This seems to occur to a lesser extent in Propata, where the relative contribution from OC NC to OC was more than twice the one in Milan.This can be related both to less stable meteorological conditions and to a cleaner and less reactive atmosphere.

Conclusions
The MWAA model was used for optical source and component apportionment of the total aerosol absorption coefficients measured at different wavelengths during wintertime at two sites with different characteristics (an urban site in the Po Valley, Milan and a rural site in the Appennines, Propata), as well as to gain information on α BrC value.
The results showed that α BrC determination was affected by lower uncertainties in Propata than in Milan, where a more complex mixture of sources can affect model performances.Nevertheless, it was shown that the application of the MWAA model by fixing α BrC led to an improvement in component apportionment.The fixed α BrC corresponded to the average value obtained for the samples where α BrC was determined with low uncertainties.A very good correlation (R 2 > 0.93) was found at both sites between b abs BrC (375 nm) and levoglucosan, identifying wood burning as the main contributor to BrC in the investigated areas.
The simultaneous component apportionment and EC measurements allowed us to determine the BC mass absorption coefficient.The latter was comparable within variability at the two sites when the role of different thermal protocols on EC quantification was considered.
OC and EC source apportionment showed that wood burning was the dominating contributor to both carbon fractions in Propata, whereas a more complex situation was detected in Milan.A relationship between samples resulting in very low α BrC value in Milan and bad OC apportionment was also apparent; in these samples, the impact of other sources can be assumed, and the two-sources scheme seems not to be applicable.In other cases, good performances were detected.
As a perspective, the application of the MWAA model to sites with different characteristics will promote the gathering of reliable information on the λ-dependence characteristics of BrC absorption properties at different sites, as well as gaining information on MAC EBC , by exploiting the ability of the model to separate different component contributions to the total b abs, together information on EC mass obtainable by other analytical techniques.

Figure 1 .
Figure 1.Scatterplot of the polar photometer PP_UniMI vs. Multi-Wavelength Absorption Analyzer (MWAA) measurements at comparable wavelengths.Deming regression lines are also represented.R > 0.98 was found in all cases.Please note that the MWAA instrument operates at 407 nm, whereas PP_UniMI operates at 405 nm for what concerns the blue light.

Figure 1 .
Figure 1.Scatterplot of the polar photometer PP_UniMI vs. Multi-Wavelength Absorption Analyzer (MWAA) measurements at comparable wavelengths.Deming regression lines are also represented.R > 0.98 was found in all cases.Please note that the MWAA instrument operates at 407 nm, whereas PP_UniMI operates at 405 nm for what concerns the blue light.
(a) BC and BrC are the only light-absorbing species in the aerosol sample, i.e., b abs (λ) = b abs BC (λ) + b abs BrC (λ), where b abs BC (λ) is the absorption coefficient due to the whole BC in the sample-with no regard to its emission sources; (b) for each component, the wavelength dependence of the absorption coefficient is proportional to λ −α , where α is component-dependent; (c) the Ångström absorption exponent of BC (α BC ) is assumed a priori.In this work α BC = 1 was set

Atmosphere 2017, 8 , 218 8 of 18 Figure 2 .
Figure 2. 5-λ aerosol absorption coefficient (babs) and the Ångström absorption coefficient (αexp) determined on the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 3 .
Figure 3. BrC Ångström Absorption exponent (αBrC) and associated fit uncertainty for the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 2 .
Figure 2. 5-λ aerosol absorption coefficient (b abs ) and the Ångström absorption coefficient (α exp) determined on the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 2 .
Figure 2. 5-λ aerosol absorption coefficient (babs) and the Ångström absorption coefficient (αexp) determined on the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 3 .
Figure 3. BrC Ångström Absorption exponent (αBrC) and associated fit uncertainty for the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 3 .
Figure 3. BrC Ångström Absorption exponent (α BrC) and associated fit uncertainty for the Propata dataset.Date referring to the beginning of the sampling is reported on the x-axis.

Figure 6 .
Figure 6.5-λ babs and αexp determined on the Milan dataset.Date and time referring to the beginning of the sampling are reported on the x-axis.

Figure 6 .
Figure 6.5-λ b abs and α exp determined on the Milan dataset.Date and time referring to the beginning of the sampling are reported on the x-axis.

Figure 6 .
Figure 6.5-λ babs and αexp determined on the Milan dataset.Date and time referring to the beginning of the sampling are reported on the x-axis.

Figure 7 .
Figure 7. αBrC and associated fit uncertainty for the Milan dataset.Date and time referring to the beginning of the sampling are reported on the x-axis.

Figure 7 .
Figure 7. α BrC and associated fit uncertainty for the Milan dataset.Date and time referring to the beginning of the sampling are reported on the x-axis.

Table 1 .
Summary of values and standard error for α BrC in samples with relative uncertainties <3%, k 1 , and k 2 .

Table 2 .
Summary of values and variability for levoglucosan/EC WB ratio, OC NC , OC FF /EC FF , OC WB /EC WB , MAC (BC), and applied thermal protocol in Propata and Milan.

Table 1 .
Summary of values and standard error for αBrC in samples with relative uncertainties <3%, k1, and k2.