Sources and formation of carbonaceous aerosols in Xi'an, China

. To investigate the sources and formation mechanisms of carbonaceous aerosols, a major contributor to severe particulate air pollution, radiocarbon ( 14 C) measurements were conducted on aerosols sampled from November 2015 to November 2016 in Xi’an, China. Based on the 14 C content in elemental carbon (EC), organic carbon (OC) and water-insoluble OC (WIOC), contributions of major sources to car-bonaceous aerosols are estimated over a whole seasonal cycle: primary and secondary fossil sources, primary biomass burning, and other non-fossil carbon formed mainly from secondary processes. Primary fossil sources of EC were further sub-divided into coal and liquid fossil fuel combustion by complementing 14 C data with stable carbon isotopic signatures. Thedominant


Introduction
Carbonaceous aerosols are an important component of PM 2.5 (particles with aerodynamic diameter < 2.5 µm), constituting typically 20 %-50 % of PM 2.5 mass in many urban ar-Published by Copernicus Publications on behalf of the European Geosciences Union.eas in China (Cao et al., 2012;R. J. Huang et al., 2014;Tao et al., 2017).The total carbon content of carbonaceous aerosols (TC) is operationally classified into elemental carbon (EC) and organic carbon (OC; Pöschl, 2005).EC is emitted as primary aerosols from incomplete combustion of biomass (e.g., wood, crop residues and grass) and fossil fuels (e.g., coal, gasoline and diesel).In addition to these combustion sources, OC has other non-combustion sources, for example, biogenic emissions, cooking, etc.Unlike EC that is exclusively emitted as primary aerosols, OC includes both primary and secondary OC (POC and SOC, respectively), where SOC is formed in the atmosphere by chemical reaction and gas-to-particle conversion of volatile organic compounds (VOCs) from non-fossil (e.g., biomass burning, biogenic emissions and cooking) and fossil sources (Jacobson et al., 2000;Kanakidou et al., 2005;Hallquist et al., 2009).Moreover, OC can be separated into water-soluble OC (WSOC) and water-insoluble OC (WIOC), according to water solubility of OC.
High concentrations of carbonaceous aerosols have been observed during severe air pollution events in China (R. J. Huang et al., 2014;Elser et al., 2016;Liu et al., 2016a, b).Knowledge and understanding of the sources and formation processes of carbonaceous aerosols, which remain unclear due to the complicated chemical composition, are highly needed to improve air quality.Clear-cut separation between fossil and non-fossil sources of carbonaceous aerosols can be successfully achieved by radiocarbon measurement (Gustafsson et al., 2009;Szidat et al., 2009;Dusek et al., 2013).Radiocarbon ( 14 C) source apportionment exploits the fact that carbonaceous aerosol emitted from fossil sources (e.g., coal combustion and vehicle emissions) does not contain 14 C, whereas carbonaceous aerosol released from nonfossil (or "contemporary") sources has a typical contemporary 14 C signature.Radiocarbon studies show that a sizeable fraction of carbonaceous aerosols are from non-fossil origins, even for aerosols collected in urban areas (Heal, 2014;Cao et al., 2017).For example, Zhang et al. (2015a) found that 48 ± 9 % total carbonaceous aerosols were contributed by non-fossil sources in urban areas of four large Chinese cities in the winter of 2013. 14C measurements conducted in early winter in 10 Chinese cities show that, on average, 65 ± 7 % total carbonaceous aerosols were derived from non-fossil sources (Liu et al., 2017).When 14 C analysis is conducted for OC and EC separately, contributions from biomass burning and other non-fossil sources to carbonaceous aerosols can be separated for a more comprehensive source apportionment.
14 C measurements on either WIOC or WSOC can help to separate primary from secondary OC from fossil sources.Fossil sources tend to mainly produce WIOC in primary emissions (Weber et al., 2007;Dai et al., 2015;Yan et al., 2017).Therefore, fossil WIOC (WIOC fossil ) can be used as a proxy of fossil POC (POC fossil ).WSOC can be directly emitted as primary aerosols mainly from biomass burning or produced as SOC.There is evidence that SOC produced through the oxidation of VOCs followed by gas-to-particle conversion contains more polar compounds and thus may be an important source of WSOC (Miyazaki et al., 2006;Sannigrahi et al., 2006;Kondo et al., 2007;Weber et al., 2007).Fossil WSOC (WSOC fossil ) therefore is thought to be a good proxy of fossil SOC (SOC fossil ). 14C analysis of WIOC and WSOC can thus provide new insights into sources and formation processes of primary and secondary OC, respectively, and has been applied in several source apportionment studies (e.g., Liu et al., 2016a, b;Dusek et al., 2017;Liu et al., 2017).For example, using this approach, Y. L. Zhang et al. (2014) found that secondary fossil OC dominates total fossil OC in a background site in southern China.Measurements in four Chinese megacities highlight the importance of secondary formation to both fossil and non-fossil WSOC in severe winter haze episodes by combining 14 C measurements of WSOC with positive matrix factorization of aerosol mass spectrometer data (Zhang et al., 2018).
14 C measurements of EC allow direct separation of fossil and biomass-burning source contributions.In addition, analysis of the stable carbon isotopic composition (namely the 13 C/ 12 C ratio, expressed as δ 13 C in Eq. 1) of EC can be used to separate fossil sources into coal and liquid fossil fuel combustion (i.e., vehicle emissions) because EC from coal combustion is, on average, more enriched in the stable carbon isotope 13 C compared to liquid fossil fuel combustion (Andersson et al., 2015;Winiger et al., 2015Winiger et al., , 2016;;Fang et al., 2018).The interpretation of the stable carbon isotope signature for OC source apportionment is more difficult because OC is chemically reactive and δ 13 C signatures of OC are not only determined by the source signatures but also influenced by chemical reactions of the organic compounds in the atmosphere (Irei et al., 2011;Pavuluri and Kawamura, 2016).
In this study, PM 2.5 samples collected from Xi'an, China, are investigated.Xi'an is the largest city in northwestern China and is also one of the most polluted cities in the world.We present, to our best knowledge, the first 14 C measurements covering all four seasons that distinguish fossil and non-fossil contributions to various carbon fractions, including EC, OC, WIOC and WSOC in Xi'an.Fossil sources of EC are further divided into coal and liquid fossil fuel combustion by complementing radiocarbon with the stable carbon isotopic signature.Concentrations of POC fossil and SOC fossil are modeled based on the 14 C-apportioned OC and EC and compared with their widely used proxies, i.e., 14 C-apportioned WIOC fossil and WSOC fossil , respectively.

Sampling
Sampling was conducted in Xi'an, China, from 30 November 2015 to 17 November 2016.PM 2.5 samples were collected on the rooftop (∼ 10 m) of a two-floor building located Atmos.Chem. Phys., 19, 15609-15628, 2019 www.atmos-chem-phys.net/19/15609/2019/ at the Institute of Earth Environment, Chinese Academy of Sciences (34.2 • N, 108.9 • E).This site is a typical urban background site surrounded by residential and education areas.The 24 h integrated PM 2.5 samples were collected from 10:00 to 10:00 LST (local standard time) the next day.PM 2.5 samples were collected on a pre-baked (780 • C for 3 h) quartz fiber filter (QM-A, Whatman Inc., Clifton, NJ, USA; 20.3 cm × 25.4 cm) using a high-volume sampler (TE-6070 MFC, Tisch Inc., Cleveland, OH, USA) at a flow rate of 1.0 m 3 min −1 .Field blank filters were treated exactly like the sample filters except that no air was drawn through the filter.
After collection, the filters were immediately removed from the sampler, packed in pre-baked aluminum foils (450 • C for 3 h), sealed in polyethylene bags and stored in a freezer at −18 • C until analysis.

Thermal-optical organic carbon (OC) and elemental carbon (EC) analysis
Filter pieces of 1.5 cm 2 were taken for OC and EC analysis using a carbon analyzer (Model 5L, Sunset Laboratory, Inc., Portland, OR, USA) following the thermal-optical transmittance protocol EUSAAR_2 (Cavalli et al., 2010).In the EU-SAAR_2 protocol the filter sample is heated stepwise in an inert helium (He) atmosphere up to 650 • C to thermally desorb organic compounds.After a rapid cooling to 500 • C the sample is heated again stepwise up to 850 • C in an oxidizing 98 % He to 2 % O 2 atmosphere to oxidize EC.All carbon gases are converted to CO 2 and detected with a nondispersive infrared (NDIR) detector.During heating in the inert He atmosphere, a fraction of OC pyrolyzes (chars) to light-absorbing EC, as demonstrated by a decreasing transmission signal.When the charred OC and original EC are released in the He/O 2 atmosphere, the transmission signal increases again.The split between OC and EC is set when the transmission signal reaches their pre-pyrolysis value.The sum of OC and EC is total carbon (TC).At the beginning of each work day, the instrument is calibrated using a sucrose standard solution.The instrument blank, representing the background contamination of the instrument during the analysis, is measured every day and negligible (TC < 0.2 µg cm −2 ) compared to the TC loading of the samples (13-246 µg cm −2 ; range).The reproducibility determined by duplicate analysis of the filter samples was within 6 % for OC and 5 % for EC.The average field blank of OC was 0.9 ± 0.2 µg cm −2 (N = 6, equivalent to ∼ 0.23 ± 0.05 µg m −3 ), which was subtracted from the sample OC concentrations.EC on field blanks was in most cases below the detection level.Details of the OC/EC measurement can also be found in Zenker et al. (2017).

Stable carbon isotopic composition of EC
The stable carbon isotopic composition of EC was measured at the Stable Isotope Laboratory at the Institute of Earth En-vironment, Chinese Academy of Sciences.To remove OC, filter pieces were heated at 375 • C for 3 h in a vacuum-sealed quartz tube in the presence of CuO catalyst grains.Extraction of EC was done by heating the carbon that remained on the filters at 850 • C for 5 h in another vacuum-sealed quartz tube.The resulting CO 2 from EC was isolated by a series of cold traps and quantified manometrically.The stable carbon isotopic composition of the purified CO 2 was determined as δ 13 C (δ 13 C EC for EC) by offline analysis with a Finnigan MAT-251 mass spectrometer (Bremen, Germany).δ 13 C values are expressed in the delta notation as per mil (‰) deviation from the international standard Vienna Pee Dee Belemnite (V-PDB): A routine laboratory working standard with a known δ 13 C value was measured every day.The analytical precision of δ 13 C was better than ±0.3 ‰ based on duplicate analyses.Details of stable carbon isotope measurements are described in our previous studies (Cao et al., 2011(Cao et al., , 2013;;Ni et al., 2018).Pyrolyzed OC can be formed through charring during the OC removal procedure and is released at the high temperature of the EC step.To assess the potential effect of pyrolyzed OC on the measured δ 13 C EC , we conducted a sensitivity analysis based on isotope mass balance (see details in Supplement S1).This analysis shows that even for high contribution from pyrolyzed OC to the isolated EC of 20 %, the expected difference in δ 13 C between measured EC and true EC is < 1 ‰.

Radiocarbon ( 14 C) measurements of OC, WIOC
and EC

Sample selection for 14 C analysis
For 14 C analysis of OC, WIOC and EC, three composite samples per season were selected to represent high (H), medium (M) and low (L) concentrations of TC to cover various pollution conditions in each season.Each composite sample consists of two to four 24 h filter pieces with similar TC loadings and air mass backward trajectories (Fig. S1 and Table S1 in the Supplement).In total, 36 radiocarbon data were measured, including 12 OC, 12 WIOC and 12 EC data. 14C values of WSOC are calculated from 14 C values of OC and WIOC according to the isotope mass balance (Eq.4).

Extraction of OC, WIOC and EC
OC, WIOC and EC extractions were conducted on our custom-built aerosol combustion system (ACS).The ACS has been described in detail by Dusek et al. (2014) and evaluated in two intercomparison studies (Szidat et al., 2013;Zenker et al., 2017).In brief, the ACS consists of a reaction  (Zhang et al., 2012;Bernardoni et al., 2013;Dusek et al., 2014).For WIOC, a waterextracted filter piece is heated at 375 • C for 10 min.Subsequently, the oven temperature is increased to 450 • C for 3 min to remove the most refractory OC that is left on the filter.However, during this step some less refractory EC might be lost.After this step, OC has been completely removed from the filter pieces.Finally, the remaining EC is combusted by heating the filter at 650 • C in O 2 for 5 min (Dusek et al., 2017;Zenker et al., 2017).EC recovery after the intermediate 450 • C step was approximately 70 %, estimated by comparing to the EC quantified by the EUSAAR_2 protocol.
Contamination during the extraction procedure is determined by following the same extraction procedures with either empty filter boat or pre-heated filters (at 650 • C in O 2 for 10 min).The contamination yields, on average, 0.85 µg OC 0.73 µg WIOC and 0.72 µg EC per extraction, respectively.Compared with our sample size of 45-210 µg OC, 45-328 µg WIOC and 15-184 µg EC, the contamination is relatively small (< 5 % of the sample amount).

14 C measurements by accelerator mass spectrometer (AMS)
14 C measurements were conducted using the Mini Carbon Dating System (MICADAS) AMS at the Centre for Isotope Research at the University of Groningen.The extracted CO 2 is released from the glass ampules and captured by a zeolite trap within a gas inlet system (Ruff et al., 2007), where the sample is diluted using He to 5 % CO 2 (Salazar et al., 2015).
The CO 2 /He mixture is directly introduced into the Cs sputter ion sources of the MICADAS at a constant rate (Synal et al., 2007).The 14 C/ 12 C ratio of an aerosol sample is usually normalized to the 14 C/ 12 C ratio of an oxalic acid standard (OXII) and expressed as fraction modern (F 14 C).Following the definition of fraction modern (Mook and van der Plicht, 1999;Reimer et al., 2004), the 14 C/ 12 C ratio of OXII is related to the unperturbed atmosphere in the reference year of 1950 by multiplying it by a factor of 0.7459: where the 14 C/ 12 C ratio of the sample and OXII are both corrected for machine background and normalized to δ 13 C = −25 ‰ with respect to V-PDB to correct for isotope fractionation.δ 13 C = −25 ‰ is the postulated mean value of terrestrial wood (Stuiver and Polach, 1977).The F 14 C values are corrected for the memory effect (Wacker et al., 2010) using alternate measurements of OXII and 14 C-free material as gaseous standards.Correction for instrument background (Salazar et al., 2015) is done by subtracting the memory-corrected F 14 C values of the 14 C-free standard.Finally, the values are normalized to the average value of the (memory-and background-corrected) OXII standards.A set of secondary standards is used to assess the robustness and reliability of the data.This includes IAEA-C7, with a consensus value of F 14 C = 0.4953±0.0012,and sample masses of 76 and 80 µg and IAEA-C8, with a consensus value of F 14 C = 0.1503 ± 0.0017 and sample masses of 63 and 100 µg.All standards including OXII and 14 C-free material used for data correction and IAEA-C7 and IAEA-C8 for quality control of AMS measurements are measured on the same day as the samples.F 14 C values of secondary standards undergo the same data correction as the samples.Results of IAEA-C7 and C8 agree within uncertainties (Table S2).
F 14 C of carbon from fossil sources is 0, and carbon from non-fossil sources (or "contemporary" sources) should have a F 14 C of 1.But the extensive release of 14 C from nuclearbomb tests in the late 1950s and early 1960s and 14 C-free CO 2 from fossil fuel combustion have perturbed the atmospheric F 14 C values significantly.The former increased the F 14 C in the atmosphere by up to a factor of 2 in the northern hemisphere in the 1960s.The nuclear tests have been banned in the atmosphere, outer space and under water since 1963.Since then, the atmospheric F 14 C has been slowly decreasing, as 14 C is mainly taken up by the oceans and terrestrial biosphere and diluted by 14 C-free CO 2 (Hua and Barbetti, 2004;Levin et al., 2010).In 2010, the F 14 C of the atmospheric CO 2 is approximately 1.04 (Levin et al., 2008(Levin et al., , 2010)), whereas in 2014 it decreased to 1.02 (Vlachou et al., 2018).

Estimation of source contributions to different carbon fractions
The F 14 C of EC, OC and WIOC (i.e., F where M OC and M WIOC are mass concentrations of OC and WIOC, respectively.M OC is measured by the thermaloptical method as described in Sect.2.2. To estimate M WIOC , we assume two extreme cases following the method of Dusek et al. (2017).( 1) WIOC is completely recovered.That is, the recovery of WIOC is 100 %, where the recovery is estimated by dividing the WIOC mass extracted using ACS (M WIOC,e ) by the WIOC mass in the aerosol samples.But the WIOC combustion temperature of 375 • C in the ACS is highly likely not high enough to recover 100 % of WIOC.Thus, this estimation is an underestimate of M WIOC (M1 WIOC ). ( 2) We assume that WIOC has the same recovery as OC.M WIOC can be calculated by dividing M WIOC,e by the OC recovery.Due to the fact that usually less WIOC than OC is lost to charring, this probably is an overestimate of M WIOC (M2 WIOC ).M WIOC is assumed to vary from M1 WIOC to M2 WIOC .The most likely value of M WIOC is chosen at M1 WIOC +2/3×(M2 WIOC −M1 WIOC ) because it is more likely that WIOC has a similar recovery as OC rather than 100 % recovery.Once M WIOC is estimated, F 14 C (WSOC) can be calculated following the Eq. ( 4).The best estimate and ranges of F 14 C (WSOC) are presented in Fig. S2 and Table S1.F 14 C (WSOC) is only slightly sensitive to M WIOC .If we shift the M WIOC from M1 WIOC to M2 WIOC , the average values of F 14 C (WSOC) only change by less than 0.03 (absolute differences).
F 14 C (EC) can be converted to the relative contribution of biomass burning to EC (f bb (EC)) by dividing by the F 14 C of biomass burning (F 14 C bb = 1.10 ± 0.05; Lewis et al., 2004;Mohn et al., 2008;Palstra and Meijer, 2014) to eliminate the effect from nuclear-bomb tests in the 1960s.F 14 C bb represents F 14 C of biomass burning, including wood burning and crop residue burning.This is because biomass burning in Xi'an mainly includes household usage of wood and crop residues as well as open burning of crop residues.F 14 C for burning of annual crop has a similar value of current atmospheric CO 2 .F 14 C of wood burning is higher than that and varies with the age of the tree.Estimates of F 14 C for wood burning are based on tree-growth models (e.g., Lewis et al., 2004;Mohn et al., 2008) and found to range from 1.08 to 1.30 relative to the wood age and felling date (Heal, 2014, and references therein).The lower limit of F 14 C bb corresponds to burning of young wood (tree that is 5-10 years old harvested between 2010 and 2015) and crop residues as main sources of EC, and the upper end of F 14 C bb corresponds to older wood (30-60 years old tree) combustion as the main source of EC.
Analogously, the relative contribution of non-fossil sources to OC, WIOC and WSOC (i.e., f nf (OC), f nf (WIOC) and f nf (WSOC), respectively) can be estimated from their corresponding F 14 C values and F 14 C nf .F 14 C nf is F 14 C of non-fossil sources including both biomass burning and biogenic emissions.F 14 C of biogenic sources can be estimated from long-term 14 CO 2 measurements at the Schauinsland background station (Levin et al., 2010(Levin et al., , 2013)).In Xi'an, biogenic OC is probably not very important, as could be expected from high concentrations of carbonaceous aerosols and strong anthropogenic sources.F 14 C nf is thus estimated as 1.09±0.05(Lewis et al., 2004;Levin et al., 2010;Y. L. Zhang et al., 2014).The central value of 1.09 corresponds to a 15 % contribution of biogenic OC to OC.
EC is primarily produced from biomass burning (EC bb ) and fossil fuel combustion (EC fossil ), and absolute EC concentrations from each source can be estimated as where f fossil (EC) is the relative contribution of fossil sources to EC, and M EC values are mass concentrations of EC.Analogously, mass concentrations of OC, WIOC and WSOC from non-fossil sources (OC nf , WIOC nf and WSOC nf , respectively) and fossil sources (OC fossil , WIOC fossil and WSOC fossil , respectively) can be determined.More detailed source apportionment of OC can be achieved by combining 14 C-apportioned OC and EC with characteristic primary OC/EC ratios for each source (i.e., using EC as a tracer of primary emissions; EC tracer method; Turpin and Huntzicker, 1995).Biomass burning usually has higher primary OC/EC ratios (r bb = 3-10) than those for coal combustion (r coal = 1.6-3) and vehicle exhausts (r vehicle = 0.5-1.3;Ni et al., 2017, and references therein).The best estimate of r bb (4 ± 1; average ± SD), r coal (2.38 ± 0.44), and r vehicle (0.85 ± 0.16) is found through a literature search as described in Ni et al. (2018) and comparable to values used in earlier 14 C source apportionment in China (Y.L. Zhang et al., 2014Zhang et al., , 2015a)).
Primary biomass burning OC (POC bb ) can be estimated by multiplying EC bb by r bb : Other non-fossil OC excluding POC bb (OC o,nf ) can be estimated as where OC o,nf includes OC from all non-fossil sources other than primary biomass burning; thus it mainly consists of secondary OC from biomass burning (SOC bb ), primary and secondary biogenic OC, and cooking emissions.In most cases, contributions of primary biogenic OC to PM 2.5 are likely small (Gelencsér et al., 2007;Guo et al., 2012).OC fossil includes both primary and secondary OC from fossil sources (POC fossil and SOC fossil , respectively): where POC fossil can be estimated from EC fossil and the primary OC/EC ratio of fossil fuel combustion (r fossil ), Fossil sources in China are almost exclusively from coal combustion and vehicle emissions; thus r fossil can be estimated as where p is the relative contribution of coal combustion to fossil EC.That is, p = EC coal /EC fossil , where estimation of EC coal is achieved by combining F 14 C (EC) and δ 13 C EC with the Bayesian calculations, as described in detail in Sect.2.6 and Supplement S2.
To propagate uncertainties, a Monte Carlo simulation with 10 000 individual calculations was conducted.For each individual calculation, F 14 C (EC) , F 14 C (OC) and F 14 C (WIOC) and concentrations of EC, OC and WIOC are randomly chosen from a normal distribution symmetric around the measured values with the experimental uncertainties as the standard deviation (SD).For F 14 C bb , F 14 C nf , r bb , r coal and r vehicle , random values of each parameter are chosen from a triangular frequency distribution, which has its maximum frequency at the central value and 0 frequency at the lower limit and upper limit of each parameter.For p values, random values from the respective probability density function (PDF) of p were used (Supplement S2).In this way 10 000 random sets of variables can be generated.For f bb (EC), f nf (OC), f nf (WIOC), f nf (WSOC), EC bb , EC fossil , OC nf , OC fossil , WIOC nf , WIOC fossil , WSOC nf , WSOC fossil , POC bb and OC o,nf , the derived average represents the best estimate, and the SD represents the combined uncertainties (Tables 1  and S3).For POC fossil and SOC fossil , the median value is considered to be the best estimate, and the interquartile ranges (25th-75th percentile) are used as uncertainties because the PDFs of POC fossil and SOC fossil are asymmetric (Fig. S3 and Table S4).

Source apportionment of EC using Bayesian statistics
Using F 14 C and δ 13 C signatures of EC (F 14 C (EC) and δ 13 C EC ) and assuming isotope mass balance in combination with a Bayesian Markov chain Monte Carlo (MCMC) scheme, it is possible to differentiate the three main sources of EC: biomass burning, liquid fossil fuel combustion (i.e., vehicle emissions) and coal combustion (Andersson et al., 2015;Li et al., 2016;Winiger et al., 2016;Fang et al., 2018).EC from fossil sources can be first separated from biomass burning by F 14 C (EC) .Furthermore, δ 13 C EC allows separation of fossil sources into coal and liquid fossil fuel burning: where the last row ensures the mass balance; f bb , f liq.fossil and f coal are the relative contribution from biomass burning, liquid fossil fuel combustion and coal combustion to EC, respectively; and F 14 C bb is the F  (Parnell et al., 2010(Parnell et al., , 2013)), where δ 13 C introduces a larger uncertainty than F 14 C. Uncertainties of δ 13 C bb , δ 13 C liq.fossil , δ 13 C coal and F 14 C bb as well as the measured ambient δ 13 C EC and F 14 C (EC) are propagated.
The results of the MCMC calculations are the posterior PDFs for f bb , f liq.fossil and f coal .The PDFs of f liq.fossil and f coal are skewed.By contrast, the PDF of f bb is symmetric, as it is well constrained by F 14 C (Fig. 6).In this study, the median is used to represent the best estimate of the f bb , f liq.fossil and f coal .Uncertainties of this best estimate are expressed as an interquartile range (25th-75th percentile) of the corresponding PDFs.The MCMC-derived f bb (calculated by Eq. 12) is very similar to that obtained directly from radiocarbon data (f bb (EC); Eq. 5), as both of them are well constrained by F 14 C.In this study, f bb and f bb (EC) are therefore used interchangeably.Details on the MCMC-driven Bayesian approach have been described in our earlier study (Ni et al., 2018).

14 C-based source apportionment of EC and OC
EC is derived mainly from fossil sources regardless of differences in EC concentrations and seasonal variations.The relative contribution of fossil fuel combustion to EC (f fossil (EC)) ranges from 69 % to 89 %, with an annual average of 82 ± 6 % (Fig. 1a).The relative contribution of fossil sources to OC (f fossil (OC)) is consistently smaller than f fossil (EC) (Fig. 1b).The values of f fossil (OC) range from 41 % to 51 %, with an annual average of 47 ± 4 %.The absolute difference in the fossil fractions between OC and EC is, on average, 35 % (28 %-42 %; range).The main reason for this difference is that biomass burning emits more OC relative to EC compared to the fossil sources (Streets et al., 2003;Akagi et al., 2011;Zhou et al., 2017).Thus, even if biomass burning contributes a small fraction to EC, it will have a much higher contribution to primary OC.Additionally other nonfossil sources, such as secondary biomass-burning emissions, primary and secondary biogenic emissions, and cooking contribute to OC but not to EC.The annual average f fossil (EC) and f fossil (OC) reported here is consistent with the results reported at an urban site of the same Chinese city in 2008-2009 (f fossil (EC) = 83 ± 5 %, f fossil (OC) = 46 ± 8 %; Ni et al., 2018), an urban site of Beijing, China, in 2013-2014 (f fossil (EC) = 82 ± 7 %, f fossil (OC) = 48 ± 12 %; Zhang et al., 2017) and 2010-2011 (f fossil (EC) = 79 ± 6 %; Zhang et al., 2015b), and a background receptor site of Ningbo, China (f fossil (EC) = 77 ± 15 %; Liu et al., 2013).Much lower f fossil (EC) and f fossil (OC) were found at a regional background site in southern China in 2005-2006 (f fossil (EC) = 38 ± 11 % and f fossil (OC) = 19 ± 10 % for Hainan; Y. L. Zhang et al., 2014), regional receptor sites in southern Asia in 2008-2009 (f fossil (EC) = 27 ± 6 % and f fossil (OC) = 31 ± 5 % for Hanimaadhoo, Maldives, and f fossil (EC) = 41 ± 5 % and f fossil (OC) = 36 ± 5 % for Sinhagad, India; Sheesley et al., 2012), where regional and local biomass burning contributes much more to carbonaceous aerosols than fossil fuel combustion and the 14 C levels can change significantly with the origin of air masses.
The f fossil (EC) and f fossil (OC) follow the same seasonal trends: the values are lower in winter and higher in the rest of the seasons (i.e., warm period).Within the warm period, both are slightly higher in spring (f fossil (EC) = 86±3 % and f fossil (OC) = 50 ± 1 %) than in summer and autumn (f fossil (EC) = 84 ± 2 % and f fossil (OC) = 47 ± 3 %) in general and also slightly lower under the cleanest periods (i.e., in spring, summer and autumn, f fossil (EC) and f fossil (OC) on polluted days -"H" and "M" samples -were higher than on clean days -"L" samples; Fig. 1; Tables 1 and S5).The low f fossil (EC) in winter is due to the substantially increased contribution from biomass burning (mainly wood burning) for heating in winter, which gradually stops in spring, but in summer and early autumn, open biomass burning (mainly crop residues) occurs in Xi'an and its surrounding areas.Some biomass burning for cooking is probably present all year-round (Huang et al., 2012;T. Zhang et al., 2014).The seasonality in biomass-burning activity is consistent with the variations in f bb (EC).f bb (EC) is higher in winter (28±4 %) than in other seasons (i.e., warm period, with an average of 15 ± 2 %).This is in line with our previous study in Xi 'an, China in 2008-2009(Ni et al., 2018).By comparison with literature data for Beijing, Beijing shows a very different seasonal trend, where f bb (EC) was lowest in summer (∼ 7 %) and increased to ∼ 20 % during the rest of the year (Zhang et al., 2017).The distinct different values and seasonality of f bb (EC) in Xi'an and Beijing indicate that biomass-burning emissions are seasonally dependent, and their influences vary spatially in different Chinese cities.The seasonal trends of f fossil (OC) were different in Beijing as well, with higher f fossil (OC) in winter than in other seasons (Yan et al., 2017;Zhang et al., 2017).This is in line with previous source apportionment results in which, during wintertime, biomass burning is a major source of OC in Xi'an and coal combustion is a dominant source for OC in Beijing (R. J. Huang et al., 2014;Elser et al., 2016).
EC concentrations from fossil fuel combustion (EC fossil ) span a range from about 0.6 to 7 µg m −3 and increase by roughly a factor of 3 from summer to winter when separately comparing clean and polluted periods.The remaining EC is contributed by biomass burning (EC bb ), which varies in a wider range than EC fossil , from about 0.1 to 3 µg m −3 (Fig. 1a and Table S3).EC fossil values are, on average, 2-3 times higher than EC bb in winter and 5-8 times higher in other seasons.This implies that the winter-summer differences in  biomass-burning emissions are larger than fossil fuel combustion emissions regardless of the fact that both biomass burning and coal combustion are expected to increase during wintertime for heating (T.Zhang et al., 2014;Shen et al., 2017;Zhu et al., 2017).OC concentrations from fossil fuel combustion (OC fossil ) range from about 1 to 20 µg m −3 , with an average of 6.8 µg m −3 , which is comparable to non-fossil OC concentrations (range: 2-28 µg m −3 ; mean: 8.2 µg m −3 ).Clear seasonal variations were observed in both EC and OC from fossil and non-fossil sources, with maxima in winter and minima in summer (Table S6).This is mainly because of an increase in coal burning and biomass burning for heating as well as unfavorable meteorological conditions in winter.

14 C-based source apportionment of water-soluble and water-insoluble OC
The fossil contribution to total WIOC (f fossil (WIOC)) varied from 49 ± 1 % in winter to 60 ± 5 % in summer, with an annual average of 55 ± 5 %.In winter the enhanced biomass burning is a source of non-fossil WIOC (Dusek et al., 2017).The relative contributions of fossil sources to WSOC (f fossil (WSOC) = 42 ± 6 %) were smaller than those to WIOC for nearly all the samples throughout the year.In winter both primary emission and secondary formation from biomass burning contribute to WSOC, and in the warm period additionally to biogenic SOC, though the latter concentrations are probably relatively low.In addition, primary fossil emissions are expected to contribute very little to WSOC, so the lower fossil fractions in WSOC are in line with expectations.In this study, the largest differences between fossil fractions in WIOC and WSOC were found to be 36 % for sample Summer-L (e.g., low TC concentrations in summer).Summer-L had the lowest f fossil (WSOC) of 28 ± 2 % (Fig. 2a), which was contrary to the stable f fossil (EC) in the warm period (Fig. 1a) and therefore cannot be explained by an increase in primary (or probably secondary) biomassburning OC.This indicates that the lowest f fossil (WSOC) for Summer-L was probably due to the impact of biogenic OC in the clean period.WSOC concentrations from non-fossil sources (WSOC nf ) are larger than WSOC from fossil sources (WSOC fossil ) at the 95 % confidence level (paired t test; P value = 0.016), with an average of 5.1 µg m −3 (range of 1.5-16.7 µg m −3 ) for WSOC nf versus an average of 3.6 µg m −3 (range of 0.6-9.4µg m −3 ) for WSOC fossil (Fig. 2).WIOC concentrations from non-fossil sources (WIOC nf ) do not differ significantly from fossil sources (WIOC fossil ; paired t test; P value = 0.113).WSOC nf , WSOC fossil , WIOC nf and WIOC fossil show the same seasonal trends, with higher mass concentrations in winter and lower concentrations in the warm period.WSOC nf is responsible for ∼ 35 % of the increased OC mass in winter, followed by WIOC nf (∼ 24 %), WIOC fossil (∼ 22 %) and WSOC ff (∼ 19 %).
Figure 2b shows the fraction of WIOC nf , WSOC nf , WIOC fossil and WSOC fossil in the total OC in different seasons.WSOC (the sum of the blue areas), on a yearly average, accounted for 60 ± 5 % of OC (ranging from 53 % to 70 %), consistent with previous measurements in Xi'an (Cheng et al., 2013;Zhang et al., 2018;Zhao et al., 2018).The remaining 40±5 % of OC is WIOC (the sum of red areas).Throughout the year, WSOC nf was the largest contributor to OC, which accounts for about one-third of the total OC, probably resulting from the mostly water-soluble biomass-burning POC and SOC as well as biogenic SOC (e.g., Mayol-Bracero et al., 2002;Nozière et al., 2015;Dusek et al., 2017).The respective proportions of WSOC fossil , WIOC fossil and WIOC nf in OC were 26 %, 21 % and 17 % on a yearly average in descending order, very likely related to secondary fossil OC, primary fossil OC and primary biomass burning, respectively (Weber et al., 2007;Dai et al., 2015;Dusek et al., 2017;Yan et al., 2017  The majority (60 %-76 %) of the non-fossil OC was watersoluble.This result is qualitatively consistent with findings reported for an urban site of Xi'an (Zhang et al., 2018) and other places such as an urban site of Beijing, China (Zhang et al., 2018), an urban or rural site in Switzerland (Zhang et al., 2013), a remote site on the island of Hainan, southern China (Y.L. Zhang et al., 2014), and two rural sites in the eastern US (Wozniak et al., 2012) and a regional background site in the Netherlands (Dusek et al., 2017).Seasonal variations in (WSOC/OC) nf ratios were also observed, with lower ratios in winter (around 0.6) and higher ratios in summer and spring (around 0.7).This reflects the higher fraction of WIOC nf in OC nf during wintertime, resulting from primary biomass-burning emissions (Dusek et al., 2017).In summer and spring, concentrations of WSOC nf and OC nf are both small, and the contribution of biogenic SOC to WSOC nf can be noticeable (Dusek et al., 2017).
The fossil OC is less water-soluble in winter, with somewhat lower (WSOC/OC) fossil ratios than in the rest of seasons (i.e., warm period).(WSOC/OC) fossil ratios in winter (0.50 ± 0.03, with a range of 0.48-0.53)fall into the lower end of the range of (WSOC/OC) fossil ratios in warm period (0.57 ± 0.08, with a range of 0.42-0.70;Fig. 3).WSOC fossil can come mainly from secondary formation and/or photochemical aging of primary organic aerosols; thus the higher (WSOC/OC) fossil ratios in the warm period suggest an enhanced SOC formation from fossil VOCs from vehicle emissions and/or coal burning.In spring and summer there is a clear increasing tend of (WSOC/OC) fossil in more polluted periods.Elevated (WSOC/OC) fossil ratios in polluted periods are very likely related to the formation of high pollutant concentrations in spring and summer.More stagnant conditions in the polluted periods (indicated by lower wind speed; see Fig. 3) that allow for accumulation of pollutants also provide more time for photochemical processes and SOC formation.As a consequence, formation of fossil WSOC will increase in stagnant conditions.At the same time, (WIOC/EC) fossil ratios decline when pollution gets worse, suggesting removal of WIOC, likely through photochemical reactions.This can shift the water-soluble versus water-insoluble distribution for fossil OC to WSOC (Szidat et al., 2009).As a consequence, the (WSOC/OC) fossil ratio is higher for Summer-H (0.62) than for Summer-L (0.42).In Xi'an, the dominant C 4 plant is the cornstalk, which is burned for cooking and heating in the areas surrounding Xi'an (Sun et al., 2017;Zhu et al., 2017).
The annually averaged δ 13 C EC is −24.9 ± 0.4 ‰ (± SD).Moderate seasonal variation in δ 13 C EC was observed, reflecting a moderate shift in the relative contributions from combustion sources throughout the year.The δ 13 C EC values in autumn (−25.3±0.2 ‰) and summer (−25.0±0.3 ‰) are most depleted and fall into the overlapped δ 13 C range for liquid fossil fuel combustion and C 3 plant burning.Because the 14 C values in autumn and summer indicate that biomass-burning contribution to EC is relatively low (∼ 16 %), we can expect that liquid fossil fuel combustion dominates EC in autumn and summer.δ 13 C EC signatures in winter (−24.8±0.2 ‰) scatter into the range for C 3 plant, liquid fossil fuel and coal combustion, implying that EC is influenced by mixed sources.The δ 13 C EC signatures in spring (−24.6 ± 0.3 ‰) overlap with both liquid fossil fuel combustion and coal combustion.Only the sample Spring-L is characterized by the most enriched δ 13 C EC value among all the samples, even more enriched than wintertime δ 13 C EC , when coal combustion for heating is expected to influence EC strongly.At the same time, higher contributions from biomass burning (i.e., lower f fossil (EC)) were observed for Spring-L.This suggests contributions from a 13 C-enriched biomass burning, that is, cornstalk burning (C 4 plant).The contribution of this regional source can become noticeable in the relatively clean air that characterizes Spring-L.
To estimate seasonal source contributions to EC, we combined all the data points from each season for the Bayesian MCMC calculations.The MCMC results (Figs. 5 and 6) show that the dominant EC source is liquid fossil fuel com- bustion (i.e., vehicle emissions).Liquid fossil fuel combustion accounts for 64 % (median; 45 %-74 %, interquartile range) of EC in autumn, 60 % (41 %-72 %) in summer, 53 % (33 %-69 %) in spring, and 46 % (29 %-59 %) in winter, respectively, in descending order.Biomass-burning EC is a small fraction of total EC throughout the year.However, the relative contribution of biomass burning to EC increased in winter (28 %; 26 %-31 %) and is comparable to the relative contribution of coal combustion (25 %; 13 %-41 %).In the warm period, coal combustion for cooking accounts for a larger fraction of EC than biomass burning.The interquartile ranges for f liq.fossil overlap with those for f coal in winter and spring (Table S7).However, comparing the PDFs distribution for both cases gives a more complete picture.As shown in Fig. 6, there is fair amount of overlap between the PDF distributions of f liq.fossil and f ocal .Though with some overlaps, in all seasons, the distribution of f liq.fossil variables are skewed to the left, while f coal is skewed to the right, with considerably higher median f liq.fossil than median f coal .
EC concentrations from biomass burning (EC bb ) increased by 9 times from summer (seasonal average of 0.2 µg m −3 ) to winter (1.8 µg m −3 ; Fig. 5b and Table S8).EC from coal combustion (EC coal ) has a 5-fold increase, from about 0.3 µg m −3 in summer and autumn to 1.6 µg m −3 in winter.
Figure 6.Probability density functions (PDFs) of the relative source contributions of (a) liquid fossil fuel combustion (f liq.fossil ), (b) coal combustion (f coal ) and (c) biomass burning (f bb ) to EC constrained by combining radiocarbon and δ 13 C measurements, calculated using the Bayesian Markov chain Monte Carlo approach.For details, see Sect.2.6.
EC from liquid fossil fuel (EC liq.fossil ) varies less strongly than EC bb and EC coal , by 4 times, from 0.7 µg m −3 in summer to 2.9 µg m −3 in winter.Liquid fossil fuel combustion (i.e., vehicle emissions) should be roughly constant throughout the year.The increased concentrations of EC liq.fossil in winter are most likely due to unfavorable meteorological conditions.An increase larger than a factor of 4 therefore suggests increasing emissions in winter.Compared to the 4fold increase in EC liq.fossil from summer to winter, EC coal only increases by 5 times in winter, reflecting the moderate seasonal variation in δ 13 C EC (Fig. 4).Coal use for heating during wintertime has been decreasing since the year 2008-2009 (Ni et al., 2018), suggested by the more depleted win-tertime δ 13 C EC in 2015-2016 than in 2008-2009 (Fig. 4).
The decreasing contribution from coal combustion to EC is consistent with the changes in energy consumption and the decreasing concentrations of coal combustion indicators (e.g., As and Pb) in Xi'an, as found in previous studies (Xu et al., 2016;Ni et al., 2018).The poor separation of fossil sources of EC into coal combustion and liquid fossil fuel combustion could be another reason, but it is difficult to quantify this effect due to our poor knowledge of δ 13 C source endmembers.

Primary and secondary OC
Based on the EC tracer method, OC o,nf is representative of SOC nf or can be considered an upper limit of SOC nf if cooking sources are significant.The fractions of primary OC (POC bb and POC fossil ) and secondary OC (OC o,nf and SOC fossil ) in total OC are shown in Fig. 7 and Table S4.On a yearly basis, the most important contributor to OC was OC o,nf (around 35 %).For all samples, OC o,nf concentrations were higher than POC bb despite the wide range of total OC concentrations in different seasons.POC bb contributed a relatively small fraction of OC (15 %-18 %) in the warm period, which increased to 22% during winter, when Xi'an was impacted significantly by biomass burning for heating and cooking.Enhanced biomass-burning activities during wintertime in Xi'an have also been reported by measurements of markers for biomass burning such as levoglucosan and K + (T.Zhang et al., 2014;Shen et al., 2017).In winter, SOC fossil was generally more abundant than POC fossil , suggesting that secondary formation rather than primary emissions was a more important contributor to total OC fossil .However, in the warm period, for OC derived from fossil fuel (POC fossil and SOC fossil ), primary emissions dominated over secondary formation (Fig. 7b and c).The SOC fossil /OC fossil ratios indicate that SOC fossil contributes roughly 57 % to OC fossil in winter versus 37 % in the warm period.However, the lower SOC fossil /OC fossil ratios in the warm period (especially in summer) than in winter in this study are unexpected due to the favorable atmospheric conditions (e.g., higher temperature and stronger solar radiation).A much higher contribution of SOC fossil to OC fossil (an annual average of around 70 %) was found in southern China (Y.L. Zhang et al., 2014).
The importance of fossil-derived SOC formation to fossil OC during wintertime was also found in other Chinese cities, including Beijing, Shanghai and Guangzhou (Zhang et al., 2015a).
As for OC from secondary origin (i.e., SOC fossil and OC o,nf ), 65±4 % is derived from non-fossil sources throughout of the year, with decreased contribution during wintertime (∼ 60 %).Using multiple state-of-the-art analytical techniques (e.g., 14 C measurements and aerosol mass spectrometry), R. J. Huang et al. (2014)  and lower non-fossil contribution to SOC (35 %-55 %) in Beijing and Shanghai in winter 2013.These findings underline the importance of the non-fossil contribution to SOC formation in Chinese megacities.The considerable differences in SOC composition in different cities might be due to the significant difference in SOC precursors from different emission sources and atmospheric processes.

Fossil WIOC versus fossil EC
Figure 8a shows a scatter plot of WIOC fossil and EC fossil concentrations.EC fossil is emitted by the combustion of fossil fuels, mainly coal combustion and vehicle emissions in Xi'an.WIOC fossil increasing concurrently with EC fossil suggests that primary emissions by fossil fuel combustion are an important source for WIOC fossil as well.However, a much higher slope of WIOC fossil against EC fossil was found in winter when compared with warm periods, implying that WIOC fossil and EC fossil originated from different fossil sources in winter and warm periods.In northern China, coal is used widely in winter for heating, which has higher primary OC/EC ratios than vehicle emissions.
The ratio of WIOC fossil to EC fossil ((WIOC/EC) fossil ) can give real-world constraints on primary OC/EC ratios of an integrated fossil source.In the warm period, individual (WIOC/EC) fossil measured in this study ranged from 0.62 to 1.1 (averaged 0.85±0.14),falling into the range of typical primary OC/EC ratios for vehicle emissions in tunnel studies (Cheng et al., 2010;Dai et al., 2015;Cui et al., 2016), excluding sample Summer-L, with the highest (WIOC/EC) fossil ratio of 1.4 (Fig. 8b).The higher (WIOC/EC) fossil for Summer-L is likely due to the less efficient removal of WIOC in cleaner periods in contrast to more polluted periods during summertime.The more stagnant conditions in more polluted periods (Fig. 3) provide longer time for photochemical processes and SOC formation, contributing to the formation of WSOC and resulting in decreased (WIOC/EC) fossil ratios, as discussed in Sect.3.2.The (WIOC/EC) fossil during wintertime averaged 1.6 ± 0.1, which is closer to the primary OC/EC ratios for coal combustion than those for vehicle emissions (Fig. 8b), suggesting that coal combustion is one important fossil source in winter other than vehicle emissions.Higher (WIOC/EC) fossil ratios in winter than in the warm period are also found in Beijing in northern China, with a (WIOC/EC) fossil ratio of 1.6-2.4 in winter versus 0.7-1.2 in the warm period (Liu et al., 2018).However, no strong seasonal trends of (WIOC/EC) fossil ratios were found in southern Chinese cities, such as Shanghai (range: 1.2-1.6;Liu et al., 2018), Guangzhou (range: 0.7-1.4;Liu et al., 2018) and Hainan (around 1; Y. L. Zhang et al., 2014).Lower (WIOC/EC) fossil ratios were found in the Netherlands (0.6±0.3; Dusek et al., 2017), Switzerland or Sweden (ranging roughly from 0.5 to 1; Szidat et al., 2004Szidat et al., , 2009)).Those higher values in China than in Europe could be attributed to the combined effects of less efficient combustion of fuel in older vehicles in China and higher primary OC/EC ratios from coal combustion that are more common in China (especially in winter in northern China) than in Europe.
In the warm period, most of individual (WIOC/EC) fossil falls in the range of primary OC/EC ratio for vehicle emissions, indicating that vehicle emission is the overwhelming fossil source, with negligible contribution from coal combustion.However, EC source apportionment by combining F 14 C and δ 13 C of EC in this study (Fig. 5) and previous studies in Xi'an (Wang et al., 2015;Ni et al., 2018) indicates that even in the warm period, coal combustion is also an important source of fine particles.Another inconsistency is that the considerable difference in (WIOC/EC) fossil between the winter and warm period suggests strong seasonal variation in coal combustion, whereas only moderate seasonal changes of δ 13 C EC were observed.Possible causes of those contradictions will be explained in the following section.and SOC (SOC fossil ), respectively (e.g., Liu et al., 2014;Y. L. Zhang et al., 2014), because primary OC from fossil sources is mainly WIOC. Figure 9 compares the mass concentrations of WIOC fossil with POC fossil as well as WSOC fossil with SOC fossil .The wider uncertainty ranges of POC fossil and SOC fossil than 14 C-apportioned WIOC fossil and WSOC fossil are mainly propagated from the wide range of primary OC/EC ratios for fossil emissions (Sect.2.5).The same trend is observed for WIOC fossil and POC fossil throughout the year (Fig. 9a).In winter, the averaged WIOC fossil concentrations of 7.1 µg m −3 (range of 3.3-10.1 µg m −3 ) matched the averaged POC fossil concentrations of 6.0 µg m −3 (range of 2.7-9.2 µg m −3 ).However, in the warm period, the WIOC fossil concentrations (1.8 µg m −3 , with a range of 0.8-5.4µg m −3 ) do not match the estimated POC fossil (2.7 µg m −3 , with a range of 0.8-7.1 µg m −3 ) equally well.WIOC fossil is still highly correlated with POC fossil but deviates strongly from the 1 : 1 line of WIOC fossil against POC fossil , with a linear regression having a slope of 1.31, an intercept of 0.32 and an R 2 of 0.92.The higher POC fossil than WIOC fossil is well outside the measurement uncertainties, at least for most samples representing high (H) and medium (M) TC concentrations (i.e., Spring-H, Spring-M, Summer-H, Autumn-H and Autumn-M).Previous studies have found that a part of the WIOC can also be secondary origin from fossil sources in Egypt (Favez et al., 2008), France (Sciare et al., 2011) and Beijing, China (Zhang et al., 2018), but this would cause the oppo-site trend (higher WIOC fossil than POC fossil ).On the other hand, measurements of fresh emissions from fossil sources show that only a small fraction (∼ 10 %) of primary fossil OC is water-soluble (Dai et al., 2015;Yan et al., 2017).The differences between POC fossil and WIOC fossil (25 %-55 %) are much larger than that, and therefore the small fraction of primary fossil WSOC cannot explain the differences between POC fossil and WIOC fossil .The best explanation for the differences in summer and spring during polluted periods is the loss of fossil WIOC, indicated by decreased (WIOC/EC) fossil when pollution gets worse.This is probably due to more stagnant conditions in polluted periods, which allows for accumulation of pollutants and also more time for photochemical processing of WIOC and SOC formation, as discussed in Sect.3.2.Evaporation of WIOC is not a likely explanation for this trend, as temperatures do not differ strongly between clean and polluted periods and partitioning to the gas phase should be stronger in clean conditions.However, this decreasing trend of (WIOC/EC) fossil with increasing TC is not found in autumn, where WIOC fossil is lower than estimated POC fossil by a roughly constant factor.In autumn, wind speed is generally low and not very variable, and photochemical processing would be weaker than in the summer and spring.

Fossil
Overall, the most likely explanation for the difference between WIOC fossil and POC fossil is the overestimate of POC fossil by the EC tracer method.POC fossil is calculated by multiplying EC fossil by primary OC/EC ratios for fos-Atmos.Chem.Phys., 19,[15609][15610][15611][15612][15613][15614][15615][15616][15617][15618][15619][15620][15621][15622][15623][15624][15625][15626][15627][15628]2019 www.atmos-chem-phys.net/19/15609/2019/sil sources (r fossil in Eq. 11).Thus, an overestimate of the POC fossil result has two causes.First, r fossil might be overestimated (as EC fossil is well constrained by 14 C), which could result either from too high an estimated fraction of coal burning in the warm period or through rapid evaporation of POC at warmer temperatures.In the warm period, semivolatile OC from fossil emission sources partitions more readily to the gas phase, leading to lower primary OC/EC ratios compared to winter.This is supported by laboratory studies and ambient observations, which find that the primary OC/EC ratio for vehicle emissions is lower in the warm period than in winter (Xie et al., 2017;X. H. H. Huang et al., 2014).Second, during longer residence time in the atmosphere, POC might not be chemically stable, and r fossil decreases with aging time in the atmosphere.This is the only mechanism that can explain the decreasing WIOC/EC fossil ratios with higher pollutant concentrations, and it is in line with findings from our earlier study that OC loss due to active photochemistry is more intense under high temperature and humidity in a warm period than in a cold winter (Ni et al., 2018).As a consequence, a good match between WSOC fossil and SOC fossil was observed in winter.As shown in Fig. 9d, the three data points fall close to the 1 : 1 line of WSOC fossil against SOC fossil .However, in the warm period, the data points fall below the 1 : 1 line of WSOC fossil against SOC fossil , with a linear regression having a slope of 0.62, an intercept of 0.01 and an R 2 of 0.92.Higher WSOC fossil than SOC fossil can be explained by underestimated SOC fossil , overestimated WSOC fossil or both.SOC fossil is calculated by subtracting POC fossil from OC fossil .Thus, underestimated SOC fossil in the warm period can result directly from overestimated POC fossil due to active OC loss.
The comparisons between WIOC fossil and POC fossil , and WSOC fossil and SOC fossil , suggest that it is feasible to use WIOC fossil and WSOC fossil as an indicator of POC fossil and SOC fossil , respectively, with respect to trends and variations in POC fossil and SOC fossil .However, the absolute concentrations of WIOC fossil and WSOC fossil are not equal to those of respective estimated POC fossil and SOC fossil , especially in the warm period.If we consider photochemical loss to be the primary reason of the differences between WIOC fossil and POC fossil , and WSOC fossil and SOC fossil , then 14 C-based WIOC fossil and WSOC fossil are probably a better approximation for primary and secondary fossil OC, respectively, than POC fossil and SOC fossil estimated using the EC tracer method (Sect.2.5, Eqs.7-10).

Conclusions
This study presents the first source apportionment of various carbonaceous aerosol fractions, including EC, OC, WIOC and WSOC in Xi'an, China, based on radiocarbon ( 14 C) measurement in four seasons for the year 2015-2016. 14C analy-sis shows that non-fossil sources are an important contributor to OC fractions throughout the year, accounting for 58 ± 6 % WSOC, 53 ± 4 % OC and 45 ± 5 % WIOC, whereas fossil sources dominated EC, with non-fossil sources contributing 18±6 % EC on the yearly average.An increased contribution of non-fossil sources to all carbon fractions was observed in winter because of enhanced non-fossil activities in winter, mainly biomass burning.Fossil sources of EC were further divided into liquid fossil fuel combustion (i.e., vehicle emissions) and coal combustion by combining radiocarbon and stable carbon signatures in a Bayesian MCMC approach.The MCMC results indicate that liquid fossil fuel combustion dominated EC over the whole year, contributing more than half of EC in the warm period and ∼ 46 % of EC in winter despite the source changes in different seasons.The remaining fossil EC was contributed by coal combustion: in winter, coal combustion (∼ 25 %) and biomass burning (∼ 28 %) equally affected EC, whereas in the warm period, coal combustion contributed a larger fraction of EC than biomass burning.
Concentrations of all carbon fractions were higher in winter than in the warm period.Non-fossil WSOC was responsible for ∼ 35 % of the increased OC mass in winter, followed by non-fossil WIOC (∼ 24 %), fossil WIOC (∼ 22 %; WIOC fossil ) and fossil WSOC (∼ 19 %; WSOC fossil ).Fossil EC and biomass-burning EC, on average, accounted for 62 % and 38 % increased EC mass in winter.Fossil WIOC/EC ratios ((WIOC/EC) fossil ) in the warm period averaged 0.85 ± 0.14, well within the range of typical primary OC/EC ratios for vehicle emissions in tunnel studies (Cheng et al., 2010;Dai et al., 2015;Cui et al., 2016).Much higher (WIOC/EC) fossil values were found in winter, with an average of 1.6 ± 0.11, which is closer to the primary OC/EC ratios for coal combustion (2.38 ± 0.44; Sect.2.5) than for vehicle emissions, indicating additional contribution from coal burning in winter.Higher (WIOC/EC) fossil in winter than in the warm period is also found in Beijing in northern China (Liu et al., 2018).However, no strong seasonal trends of (WIOC/EC) fossil were found in southern China, such as Shanghai (Liu et al., 2018), Guangzhou (Liu et al., 2018) and Hainan (Y.L. Zhang et al., 2014), where there is no official heating season using coal.
The majority (60 %-76 %) of the non-fossil OC was watersoluble in all seasons, probably resulting from the mostly water-soluble biomass-burning POC and SOC and biogenic SOC.The fossil OC in winter is less water-soluble than in the warm period, suggesting an enhanced SOC formation from fossil VOCs from vehicle emissions and/or coal burning in the warm period.In spring and summer, there is a clear increasing trend of (WSOC/OC) fossil and decreasing trend of (WIOC/EC) fossil in more polluted conditions.This suggests that the fossil WSOC formation as well as fossil WIOC removal increase under the stagnant conditions that characterize polluted periods and allow for accumulation of pollutants and also photochemical processing and secondary OC formation.WIOC fossil and WSOC fossil have been used widely as proxies of the primary and secondary fossil OC, respectively, since primary fossil sources tend to produce mainly WIOC.In winter, mass concentrations of WIOC fossil were comparable to POC fossil , and concentrations of WSOC fossil were comparable to SOC fossil , where POC fossil and SOC fossil are estimated using the EC tracer method.However, the agreement was worse in the warm period even though the respective concentrations were highly correlated.In other words, variations in WIOC fossil and WSOC fossil follow similar trends as POC fossil and SOC fossil , respectively.However, the absolute concentrations of WIOC fossil and WSOC fossil are not equal to those of estimated POC fossil and SOC fossil , especially in the warm period.The higher mass of POC fossil than WIOC fossil in the warm period was probably due to overestimated POC fossil (thus underestimated SOC fossil ) resulting from overestimated primary fossil OC/EC ratios.
In the warm period, at relatively high temperatures, semivolatile OC from emission sources becomes volatilized more quickly, owing to higher temperatures; this leads to lower primary OC/EC ratios than in winter and is in line with the laboratory and ambient observations that the primary OC/EC ratio for vehicle emissions is lower in the warm period than in winter (Xie et al., 2017;X. H. H. Huang et al., 2014) and the findings from our earlier study that in the warm period, photochemical OC loss is active and affects final OC concentrations (Ni et al., 2018).We suggest that WIOC fossil and WSOC fossil are probably a better approximation for primary and secondary fossil OC, respectively, than POC fossil and SOC fossil estimated using the EC tracer method.
Data availability.All data needed to evaluate the conclusions in this study are present in the paper and the Supplement.Additional data related to this paper are available upon request to the corresponding author.
Author contributions.UD, RJH, HN and JC designed the study.HN and HD conducted the 14 C measurements.HN, HD and UD interpreted the 14 C data.JG performed the measurements of stable isotope 13 C. HN and UD interpreted the 13 C data.HN and UD prepared the figures, and HN wrote the paper.All authors commented on and discussed the paper.
Competing interests.The authors declare that they have no conflict of interest.

Figure 1 .
Figure 1.(a) Mass concentrations of EC from fossil and non-fossil sources (EC fossil and EC bb , respectively), and fraction of fossil in EC (f fossil (EC)).(b) Mass concentrations of OC from fossil and non-fossil sources (OC fossil and OC nf , respectively), and fraction of fossil in OC (f fossil (OC)).

Figure 2 .
Figure 2. (a) Mass concentrations of WIOC and WSOC from fossil and non-fossil sources (WIOC fossil , WIOC nf , WSOC fossil and WSOC nf ) as well as fraction of fossil in WIOC and WSOC (f fossil (WIOC) and f fossil (WSOC), respectively).(b) Averaged relative contribution to OC (%) from WIOC nf , WSOC nf , WIOC fossil and WSOC fossil in each season.

Figure 3 .
Figure 3. (a) Wind speed for each composite sample.Each composite sample consists of two to four 24 h filter samples, and each filter sample is shown as individual data point.The wind speed is recorded by the Meteorological Institute of Shaanxi Province, Xi'an, China.(b) The fraction of fossil WSOC in fossil OC ((WSOC/OC) fossil ; dark blue circles); the ratio of fossil WIOC to fossil EC ((WIOC/EC) fossil ; black squares) over all the selected samples throughout the year.

Figure 4 .
Figure 4. 14 C-based fraction fossil versus δ 13 C for EC in Xi'an, China, in different seasons in 2015-2016 (this study; circle symbols) compared with those in winter 2008-2009 from Ni et al. (2018; square symbols).The size of the symbols for the year 2015-2016 (this study) represents the pollution conditions (high, medium and low) for each sample.The symbol size for the years 2008-2009 does not correspond to pollution conditions and is indicated by "NA".The expected 14 C and δ 13 C endmember ranges for emissions from C 3 plant burning, liquid fossil fuel burning and coal burning are shown as green, black and brown bars, respectively.The δ 13 C signatures are indicated as mean ± SD (Sect.2.6).The δ 13 C signatures of cornstalk (i.e., C 4 plant) burning (−16.4 ± 1.4 ‰) are also indicated.

Figure 5 .
Figure 5. (a) Fractional contributions of three incomplete combustion sources to EC in different seasons.(b) Mass concentration of EC (µg m −3 ) from each combustion source.The data are presented in TablesS7 and S8.

Figure 7 .
Figure 7. (a) Estimated mass concentrations of POC bb , OC o,nf , POC fossil and SOC fossil (µg m −3 ) in total OC of PM 2.5 samples.The error bars indicate the interquartile range (25th-75th percentile) of the median values.(b) The percentage of POC bb , OC o,nf , POC fossil and SOC fossil in total OC.(c) Average source apportionment results of OC in each season and over the year.The numbers below the pie charts represent the seasonally and annually averaged OC concentrations.
Figure 8.(a) Scatter plot of EC concentrations from fossil sources (EC fossil ) versus WIOC concentrations from fossil sources (WIOC fossil ) in winter (circle) and the warm period (square).(b) WIOC-to-EC ratio from fossil sources ((WIOC / EC) fossil ) over all the selected samples throughout the year.The dashed areas indicate typical primary OC / EC ratios for coal combustion (brown) and vehicle emissions (black).

Figure 9 .
Figure 9. (a) Concentrations of WIOC and POC from fossil sources (WIOC fossil and POC fossil , respectively).(a) has the same x axis as (b).(b) Concentrations of WSOC and SOC from fossil sources (WSOC fossil and SOC fossil , respectively).(c) Scatter plot of WIOC fossil concentrations versus POC fossil concentrations.(d) Scatter plot of WSOC fossil concentrations versus SOC fossil concentrations.The interquartile range (25th-75th percentile) of the median POC fossil and SOC fossil is shown by grey vertical bars in (a) and black vertical bars in (b).
www.atmos-chem-phys.net/19/15609/2019/Atmos.Chem.Phys., 19, 15609-15628, 2019 14C of biomass burning (1.10 ± 0.05), as mentioned in Sect.2.5.F 14 C liq.fossil and F 14 C coal are zero due to the long-term decay.δ 13 C bb , δ 13 C liq.fossil and δ 13 C coal are the δ 13 C signature of EC emit-extent with the range of δ 13 C coal , although liquid fossil fuels are usually more depleted than coal.The MCMC technique takes into account the variability in the source signatures of F 14 C and δ 13 C coal (−23.4 ± 1.3 ‰) are compiled and establishedNi et al., 2018)tudies in previous publications(Andersson et  al., 2015, and references therein;Ni et al., 2018).The source endmembers for δ 13 C are less well constrained than for F 14 C, as δ 13 C varies with fuel types and burning conditions.For example, the range of possible δ 13 C liq.fossil overlaps to a small Atmos.Chem.Phys.,19,[15609][15610][15611][15612][15613][15614][15615][15616][15617][15618][15619][15620][15621][15622][15623][15624][15625][15626][15627][15628]2019www.atmos-chem-phys.net/19/15609/2019/ Ni et al. (2018)es apportioned by stable carbon isotopesAlong with radiocarbon data, the stable carbon isotopic ratio of EC (denoted by δ 13 C EC ) provides additional insight into source apportionment of EC, especially between different types of fossil sources (i.e., coal versus liquid fossil fuel combustion).Figure4shows 14 C-based f fossil (EC) against δ 13 C EC in Xi'an in different seasons for 2015-2016 from this study and in winter for 2008-2009 fromNi et al. (2018), together with the ranges of endmembers (i.e., isotopic signature) for the different EC sources of coal combustion, liquid fossil fuel combustion and biomass burning (C 3 and C 4 plants).f fossil (EC) is well constrained by F 14 C (EC) , clearly separating fossil sources from biomass burning.In contrast to 14 C, the source endmembers (i.e., isotopic signature) for δ 13 C are less well constrained, and δ 13 C values for liquid fossil fuel combustion overlap with δ 13 C values for both coal and C 3 plant combustion.Regardless of the changes of δ 13 C EC in different seasons, all the δ 13 C EC data points fall within the range of C 3 plant burning, coal and liquid fossil fuel, indicating that the C 3 plant is the dominating biomass type in Xi'an, with little influence from C 4 plant burning.