An evaluation of source apportionment of fine OC and PM2.5 by multiple methods: APHH-Beijing campaigns as a case study

evaluation of source apportionment of fine OC and by methods: APHH-Beijing campaigns as a case study', Faraday This study aims to critically evaluate the source apportionment of ﬁ ne particles by multiple receptor modelling approaches, including carbon mass balance modelling of ﬁ lter-based radiocarbon ( 14 C) data, Chemical Mass Balance (CMB) and Positive Matrix Factorization (PMF) analysis on ﬁ lter-based chemical speciation data, and PMF analysis on Aerosol Mass Spectrometer (AMS-PMF) or Aerosol Chemical Speciation Monitor (ACSM-PMF) data. These data were collected as part of the APHH-Beijing (Atmospheric Pollution and Human Health in a Chinese Megacity) ﬁ eld observation campaigns from 10 th November to 12 th December in winter 2016 and from 22 nd May to 24 th June in summer 2017. 14 C analysis revealed the predominant contribution of fossil fuel combustion to carbonaceous aerosols in winter compared with non-fossil fuel sources, which is supported by the results from other methods. An extended Gelencs´er (EG) method incorporating 14 C data, as well as the CMB and AMS/ACSM-PMF methods, generated a consistent source apportionment for fossil fuel related primary organic carbon. Coal combustion, tra ﬃ c and biomass burning POC were comparable for CMB and AMS/ ACSM-PMF. There are uncertainties in the EG method when estimating biomass burning and cooking OC. The POC from cooking estimated by di ﬀ erent methods was poorly correlated, suggesting a large uncertainty when di ﬀ erentiating this source type. The PM 2.5 source apportionment results varied between di ﬀ erent methods. Through a comparison and correlation analysis of CMB, PMF and AMS/ACSM-PMF, the CMB method appears to give the most complete and representative source apportionment of Beijing aerosols. Based upon the CMB results, ﬁ ne aerosols in Beijing were mainly secondary inorganic ion formation, secondary organic aerosol formation, primary coal combustion and from biomass burning emissions.


Introduction
Fine particulate matter (PM 2.5 ) has adverse effects on atmospheric visibility and human health, and inuences the climate. 1,2In Beijing, PM 2.5 pollution remains a major challenge with its hourly concentration reaching as high as 438 mg m À3 during the APHH-Beijing (Atmospheric Pollution and Human Health in a Chinese Megacity) winter campaign. 3Source apportionment of PM 2.5 provides important information for developing more effective pollution control strategies.
Receptor modelling methods such as Positive Matrix Factorization (PMF), Chemical Mass Balance (CMB) and UNMIX have been widely applied for the source apportionment of PM 2.5 . 4For the CMB model, aerosol chemical composition data from the sources and the receptor site are needed.It constructs the best-t linear combination of the chemical compositions of source proles to match the ambient particle composition. 5The selection of source proles requires a good understanding of the likely sources contributing to PM at the sampling site.The CMB model can provide the most reliable results when each source is well characterized with a constant chemical composition.The inherent uncertainties in using this model derive mainly from errors in the measurement of chemical species and the selection of source proles.If the source prole is unrepresentative or not included, then the source apportionment results are less trustworthy.CMB has been applied in many studies and has been conrmed to be a good tool for apportioning primary sources of carbonaceous aerosols. 6,7MF is a receptor model which does not require any prior information about source proles.It is a bilinear unmixing model which assumes that its dataset matrix comprises a linear combination of factors. 8The factor proles should be constant and varied in species concentrations with all values constrained to be positive in the model.The number of factors is not xed, and the modeler needs to select the optimal number of factors for the best interpretation of the data.This is considered as the least quantitative step in PMF analysis, as it largely depends on subjective judgements and the skills of the user. 9,10In addition, linear transformations (rotations) of the factors may also complicate the results and increase the uncertainties.Brown et al. 11 reported methods for estimating the uncertainties in PMF solutions.Another shortcoming of the PMF method is that it requires a large number of samples for analysis, while CMB can be applied to only a few ambient samples, and in theory even a single sample.
In addition to the application of PMF to datasets from integrated air samples, PMF can also be applied to continuous Aerodyne Aerosol Mass Spectrometer (AMS) or Aerosol Chemical Speciation Monitor (ACSM) datasets (AMS/ACSM-PMF).][14] Unlike some atmospheric datasets which include OC/EC, metals and inorganic ions, measured by multiple instruments, an advantage of AMS/ACSM-PMF is that the measurement error is more coherent as the data were obtained from a single instrument.However, these online datasets are also accompanied by uncertainties in the determination of the relative ionisation efficiencies (RIEs) and collection efficiencies (CEs). 15Accurate knowledge of RIEs and CEs is important for quantication, and this information is not always available. 16Through investigation of the dominant peaks at representative m/z resulting from significant fragmentation following vaporization and ionization in the AMS/ACSM, organic aerosol (OA) sources including primary (coal combustion, biomass burning, traffic, cooking) and generic secondary sources can be identied by PMF factor analysis. 8,131][22] It can quantitatively differentiate atmospheric carbonaceous aerosols from fossil fuels and from contemporary biomass, as fossil fuels are devoid of 14 C while modern biomass carbon has a wellrecognized 14 C/ 12 C ratio. 23The advantage of this approach is that this ratio is an intrinsic property of the carbonaceous aerosol, which is independent of concentration, unlike molecular tracers. 23It is considered as a robust method to unambiguously distinguish fossil and non-fossil sources of carbonaceous particles. 21,24The disadvantage is that 14 C measurements are mainly conducted on total carbon (TC), organic carbon (OC) and elemental carbon (EC), and they require a large mass of sample to be analysed in order to apportion specic compounds like PAHs or fatty acids. 25,26 14C measurements can be combined with molecular tracers (i.e.levoglucosan for biomass burning, arabitol/mannitol for fungal spores), and OC/EC emission ratios from the literature for distinguishing natural or anthropogenic or more specic sources. 27,28ince each method has its own uncertainties and limitations for source apportionment, it is important to compare the results from different methods in order to better understand the source apportionment results.Szidat et al. (2018) 29 combined the results from 14 C analysis with those from AMS-PMF, and quantied fossil and non-fossil secondary organic aerosols (SOAs).Ke et al. (2007) 30 compared 14 C and CMB results and found comparable results for fossil and contemporary source-derived primary carbon.Huang et al. (2013) 31 found good correlation for the SOAs estimated from the OC/EC ratios and those estimated by AMS-PMF in summer, but the OC/EC method overestimated SOAs in winter due to more biomass burning activities.Yin et al. 4 compared CMB and AMS-PMF results and found a generally good correlation between the two methods, but the contributions of some individual organic aerosol sources were different.Bullock et al. 32 apportioned the sources of PM by applying both CMB and PMF to the same dataset, suggesting that the model results are strongly affected by the selection of molecular tracers and source proles.Most of the comparisons so far were only done between two methods.
In this study, we provide a critical comparative evaluation of the source apportionment results from multiple RM methods applied to a dataset generated from the APHH-Beijing eld campaigns in Beijing as a case study.

Methodology
2.1 Field campaigns PM 2.5 samples were collected at an urban site and a rural site in Beijing during winter (10 th November to 12 th December 2016) and summer (22 nd May to 24 th June 2017) campaigns as part of the APHH-Beijing programme. 3The urban site (39.98 N, 116.39 E) is located at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences in Beijing, China, while the rural site (40.17N, 117.05 E) is in a village in Pinggu (PG) District.An AMS was deployed at the urban site during both campaigns and an ACSM was deployed at the rural site in winter only.The details of this eld campaign can be found elsewhere. 3,332 Offline sample analyses PM 2.5 samples were characterized by IC for inorganic ions, ICP-MS for trace metals, XRF for crustal elements, a DRI2015 analyzer for OC and EC, and GC-MS for organic tracers.The 14 C in total carbon (TC), EC and water insoluble OC was determined for 13 IAP samples and 12 PG samples by using an accelerator mass spectrometer.34,35 More details of the analytical methods are given in the ESI † and elsewhere.36,37

Extended Gelencsér (EG) method
The method of Gelencsér et al. (2007) 38 was developed further to incorporate radiocarbon data for source apportionment of OC and EC from biomass burning, cooking and secondary organic aerosols.In Hou et al. (2020), 39 the 14 C results were combined with the OC/EC ratios in different sources to apportion the OC into primary OC from fossil fuels, biomass burning and cooking, and secondary OC, and this method is referred to as the extended Gelencsér (EG) method.The uncertainties of the EG method mainly come from measurement errors and the inferred constituent ratios like OC/EC for different sources.Details of the Gelencsér method and the extended Gelencsér method are provided in Table S1.†

Chemical mass balance (CMB) modelling
A receptor modelthe chemical mass balance (US EPA CMB8.2)was applied for ne OC source apportionment.CMB modelling for the IAP and PG sites was conducted separately using the same source proles mainly obtained from China.Experimental details are provided in Xu et al. (2020) 36 and Wu et al. (2020) 37 for IAP and PG, respectively.

Positive matrix factorization (PMF) modelling
PMF modelling was conducted both for lter-based data and for online AMS data and ACSM data. 8,40For lter-based data, 133 samples from both sites in winter and summer were combined for PMF modelling.The AMS and ACSM data analysis details are described elsewhere. 14The application of PMF to speciated chemical data from off-line lter samples is described by Srivastava et al. (2020). 41 Results and discussion

Comparison of OC source apportionment results by different methods
The contribution of fossil and non-fossil sources to TC, OC and EC was analysed through 14 C analysis (Fig. S1 †).Generally, non-fossil fuel sources accounted for 41% of TC, which is comparable with the percentage reported in another study conducted in Beijing (45%). 42The concentration of non-fossil fuel derived OC (OC nf ) was 19.7 AE 11.5 mg m À3 at PG in winter, more than two times that at IAP in winter (8.6 AE 4.7 mg m À3 ), while for OC nf in summer, the two sites were not signicantly different.The concentration of fossil fuel derived OC (OC f ) was much higher than that of OC nf in winter, while the concentration of OC f in summer was close to that of OC nf at both sites.The extended Gelencsér method further separated OC into POC nf , POC f , SOC nf and SOC f .POC nf was also separated into biomass burning (POC bb ) and cooking (POC ck ).However, due to the limited number of samples used for 14 C analysis, the results from the EG method may not be representative of the whole sampling period.Hence, we compared the source apportionment results from CMB, PMF and AMS/ACSM-PMF rst, as presented in Fig. 1.The results from all 4 methods for samples obtained on identical days will be discussed later (Table 2).
AMS/ACSM-PMF apportioned OC into traffic (HOC), coal combustion (CCOC), biomass burning (BBOC), cooking (COC) and SOC (i.e., OOC).In addition to these sources, the CMB model can also differentiate gasoline and diesel emissions in the traffic source category.Vegetative detritus is a minor source of OC in PG which was only resolved by the CMB model.PMF of lter-based data resulted in 7 factors: coal combustion, traffic, oil combustion, biomass burning, secondary inorganic ions, road dust and soil dust, in which road and soil dust were combined into a single dust source.
The reconstructed OC (sum of OC in each source category) in the middle of the pie charts (Fig. 1) for CMB was the same as the measured OC; the differences in concentration level between the reconstructed OC and the observed OC in Table 1 were because a small number of samples were not included in the CMB modelling due to insufficient speciation data.The reconstructed OC masses in NR-PM 1 for the AMS/ACSM-PMF data were comparable with those in PM 2.5 for CMB.This agrees in general with Guo (2016) 43 that OC fractions in ne particles are mostly concentrated in particles <1 mm; in addition, there are some uncertainties in converting organic aerosols (OAs) into OC in the AMS/ACSM-PMF results using OA/OC ratios from the literature (ESI †).The reconstructed OC for PMF was mostly lower than that for the other methods, which is due to the inability of PMF to model heavily polluted events.In the CMB source apportionment results, seven primary sources explained 56.1-75.7% of OC at IAP and PG in both seasons.The unexplained OC (other OC) was considered to be mostly SOC based on the good correlation (R 2 : 0.6-0.7;slope: 1.0 AE 0.2) between the "other OC" and the SOC estimated based on OC/EC ratios. 36PMF did not resolve SOC but yielded a factor for secondary inorganics, which may contain some secondary OC.In winter, fossil fuel (the sum of diesel, gasoline, industrial and residential coal combustion) related POC f contributed 46.9% and 44.0% of OC at IAP and PG, respectively, according to the CMB results.For PMF, the fossil fuel sources (the sum of traffic, oil and coal combustion) contributed 57.7% and 60.1% of OC at IAP and PG, respectively.The higher percentages for PMF may be because PMF did not separate well the POC and SOC.HOC was not resolved at the IAP site by AMS-PMF, hence, fossil fuel related POC (CCOC) contributed only 19.9% of OC, while its contribution (the sum of CCOC and HOC) at the PG site (51.4%) was similar to that for CMB and PMF.Coal combustion contributed 20-35% of OC for CMB and AMS/ACSM-PMF at both sites in winter.The much higher contribution (around 50%) for PMF could be the result of unseparated POC and SOC.For CMB, traffic emissions (diesel and gasoline) contributed 11.9% and 19.7% at IAP and PG, respectively, which are close to the values for AMS/ACSM-PMF (HOC), but much higher than the values for PMF.Biomass burning was resolved by all methods; it contributed from 15.8% to 17.8% of reconstructed OC at IAP, and 12.0% to 18.5% of reconstructed OC at PG for CMB, PMF and AMS/ACSM-PMF.Cooking was not identied in the PMF factors and its contributions to OC resolved by CMB (10.3% and 1.3% for IAP and PG, respectively) were different to those resolved by AMS/ACSM-PMF (18.5% and 12.9% for IAP and PG, respectively).
In summer, the estimated contributions of primary sources of OC varied signicantly for the three methods.Dust related OC was a dominant contributor in the PMF results, which is doubtful.The dust factor was probably associated with SOC as this factor was observed with the second highest concentrations of nitrate and sulfate, aer the factor of secondary inorganics.The contribution of fossil fuel sources to OC is similar for the CMB (45.4%) and PMF (48.6%) analyses at PG.Other sources such as cooking and biomass burning also varied for the different methods. 14C was determined in 25 samples.For consistency, the source apportionment results from CMB, PMF and AMS/ACSM-PMF for the 25 samples were singled out for further comparison (Table 2).More details of the source apportionment results from the 4 methods can be found in Tables S2-S5.† The EG method was not able to quantify POC from traffic and coal combustion, but a maximum value for traffic related POC (POC tra ) can be estimated by multiplying EC f by the OC/EC ratio for primary traffic emissions (0.85 AE 0.16) in China, 44 assuming that EC f only originates from traffic emissions.A minimum value for coal combustion related POC can be subsequently calculated by subtracting the maximum POC tra from POC f .In general, the average reconstructed OC concentrations were comparable for the four methods on identical days, except for PMF at PG during winter.The POC f estimated by CMB was on average 1.1, 1.3, 1.2 and 1.6 times higher than the EGbased results for IAP and PG in winter and summer, respectively.For the EG method, POC f was estimated as EC f multiplied by the ratio of OC/EC f,min .The signicantly lower POC f estimated by the EG method at PG in summer is due to the relatively low OC/EC f,min ratios used for the calculation.The much lower estimates of POC f at IAP by AMS/ACSM-PMF were due to the failure of AMS/ACSM-PMF to resolve either HOC or CCOC.When HOC and CCOC were both resolved at PG during winter, the POC f estimated by AMS/ACSM-PMF was comparable with that estimated by CMB.Coal combustion (POC cc ) differed for the 4 methods except for the comparable results for the EG method and CMB at IAP and PG during winter.The traffic related POC (POC tra ) results were consistent for CMB, EG and AMS/ACSM-PMF in summer, but the EG method provided different results in winter.The maximum POC tra for the EG method was much lower than that for CMB and AMS/ACSM-PMF.This could be due to the use of an unrepresentative OC/EC ratio for primary traffic emissions (0.85 AE 0.16) in China, 44 which may be seasonally variable.This ratio should be higher in winter than in summer because faster catalyst and engine warm-up times and more volatilization of semivolatile organic compounds in summer will cause a decrease in the OC/EC ratio in traffic emissions. 45Hence, POC tra in winter may be underestimated by the EG method.AMS/ACSM-PMF only resolved POC bb in the wintertime and the results were generally similar to the CMB results, while the values obtained by the EG method and PMF were much lower.In the summertime, the POC bb contributions estimated by the EG method and CMB were very close, but that estimated by PMF was extremely low.A discrepancy was also found for cooking (POC ck ), where the estimated contributions were only comparable for the EG method and AMS/ ACSM-PMF at PG during winter and IAP during summer.The sum of POC bb and POC ck in AMS/ACSM-PMF at IAP during winter was 9.9 AE 6.5 mg m À3 , which was higher than the OC nf (POC bb + POC ck + SOC nf ; 8.6 AE 4.7 mg m À3 ) measured through 14 C analysis, suggesting that the sum of POC bb and POC ck in AMS/ACSM-PMF was overestimated at IAP during winter.The overestimation of POC ck could be due to the use of a relatively low OA/OC ratio for the cooking source or a low RIE for cooking OAs (1.4) in AMS.The actual RIE could be higher, for example 1.56-3.06as reported in another study. 46he results from the four methods are further compared through correlation analysis and discussed in Section 3.3.Due to the absence of ACSM-PMF data at PG during summer, the comparisons were conducted on the 20 samples for which all methods gave results.In addition, the OC source apportionment results from the four methods for haze samples (n ¼ 11) and non-haze samples (n ¼ 9) are Fig. 2 Source contributions to OC on haze (grey) and non-haze (white) days in Beijing estimated by CMB, the EG method, PMF and AMS/ACSM-PMF (note: the OC in the middle of the pie chart is the reconstructed OC, which is the sum of the OC from each source; VD: vegetative detritus; BB: biomass burning; CC: coal combustion; OOC: oxidized OC; CCOC: coal combustion OC; BBOC: biomass burning OC; COC: cooking OC; HOC: hydrocarbon-like (traffic) OC).compared in Fig. 2. On haze days, CMB and AMS/ACSM-PMF were consistent in apportioning OC into POC f , POC nf and SOC.The POC f estimated by the EG method was consistent with that estimated by CMB and AMS/ACSM-PMF, but SOC was much higher for the EG method than the others, and POC nf was lower for the EG method than for CMB and AMS/ACSM-PMF.Coal combustion and biomass burning OC were also comparable in the CMB and AMS/ACSM-PMF results.Cooking was more difficult to resolve as mentioned above.The reconstructed OC (34.4 mg m À3 ) for PMF was much lower than those (42.7-44.4mg m À3 ) for the other methods, indicating that PMF had problems resolving OC sources in haze samples.The PMF factors were also less comparable with the sources estimated by the other methods, except for BB.On non-haze days, the factors in the four methods were less comparable, suggesting the difficulty of OC source apportionment for non-haze samples, especially by PMF.The dust factor in PMF could be associated with SOC based on the comparison with the other methods.

Correlation analysis
An orthogonal regression analysis was conducted on the results from CMB, the EG method and AMS/ACSM-PMF for identical days.The PMF results are not compared here because the method did not separate POC and SOC and its results differed the most from those of the other methods.
3.3.1Primary OC from fossil fuel combustion (POC f ).For the EG method, POC f was calculated by multiplying EC f by the estimated minimum (OC/EC) f ratios at both sites during winter and summer.POC f was calculated from the CMB results as the sum of gasoline, diesel, industrial and residential coal combustion, while for AMS/ACSM-PMF, POC f was the sum of HOC and CCOC.The orthogonal regression results for POC f estimated by the three methods are plotted in Fig. 3.
In the comparison of POC f estimated by the three methods, strong correlations (r 2 > 0.6) were found between them with slopes ranging between 0.78-1.26.The CMB-resolved POC f was found to be signicantly correlated (r 2 > 0.8) with those from the other two methods (Fig. 3).When excluding the two extreme datapoints (POC f -AMS/ACSM-PMF > 30 mg m À3 ), the POC f estimated by the EG method and AMS/ACSM-PMF were also highly correlated with r 2 of 0.77 and slope of 0.82.This probably suggests a bigger uncertainty for AMS/ACSM-PMF in estimating POC f at high concentrations.For the coal combustion POC estimated by CMB and AMS/ ACSM-PMF, the slope was close to unity with r 2 of 0.45 (Fig. S2(a) †).For POC tra estimated by the two methods, the concentrations were generally consistent (Table 2) and well correlated with r 2 of 0.91 and slope of 0.87 (Fig. S2(b) †).But there is no correlation between the two methods at IAP during summer (Fig. S11(d) †).It is challenging to apportion POC tra when the concentrations are low.
3.3.2Primary OC from biomass burning (POC bb ).The correlations of POC bb estimated by the three methods are shown in Fig. 4. The POC bb estimated by CMB was mainly characterized by high concentrations of anhydrous sugars like levoglucosan, while POC bb in AMS/ACSM-PMF was identied by prominent peaks at m/z 60 and 73, which are typical fragments of anhydrous sugars like levoglucosan. 47The POC bb results from both methods were comparable with a slope of 0.99 and r 2 of 0.54.POC bb was estimated by the EG method using the OC/levoglucosan and EC/OC ratios (ESI †).The EG results correlated well with those from CMB (r 2 ¼ 0.86), but the absolute concentration of POC bb estimated by the EG method was only approximately 50% of that estimated by CMB in winter at IAP (4.4 AE 2.5 mg m À3 ) and PG (9.2 AE 5.5 mg m À3 ) (Table 2).In summer, when the POC bb contribution was signicantly lower than that in winter, the POC bb estimated by the EG method was comparable with that estimated by CMB at IAP, and much higher than that estimated by CMB at PG.In this study, different OC/levoglucosan and EC/OC ratios were applied when calculating POC bb by the EG method.The ratios were obtained from sowood for the winter and summer campaign and maize straws in winter but from sowood and wheat straws in summer aer analysing the corresponding relationship of levoglucosan with mannosan and galactosan.Besides, levoglucosan was reported to be less stable in summer due to a higher degradation rate, especially under high relative humidity conditions. 48Hence, the EG method may introduce uncertainties in the POC bb concentrations due to various factors, for example uncertainty in the OC/levoglucosan ratios.The correlation results for the three methods at IAP and PG during winter and summer are provided in Fig. S3.† Good correlations were found between the EG method and the other two methods at both sites, but the absolute POC bb concentrations estimated by the EG method are different to those from the other methods.

Primary OC from cooking (POC ck ).
The CMB results for POC ck were mainly characterized by high concentrations of palmitic and stearic acids, which are the predominant compounds in cooking emissions. 49The POC ck estimated by AMS/ACSM-PMF was characterized by high peaks for the fragment ions C 3 H 3 O + , C 4 H 7 + , C 3 H 5 O + , and C 4 H 9 + at m/z 55 and 57 in the mass spectrum. 50No correlation between the three methods was observed for POC ck , as shown in Fig. 5. POC ck was estimated by the EG method as the difference between POC nf and POC bb , and other biogenic POC was neglected.Hence, POC ck could be overestimated by the EG method.8][19] Elser et al. 51 proposed the use of a multilinear engine (ME-2) controlled via a source nder (SoFi) to improve the source apportionment results obtained by PMF of AMS data.Abdullahi et al. 52 applied CMB for the source apportionment of atmospheric aerosols using the chemical proles of molecular markers such as alkanes, PAHs, acids, and sterols from four different styles of cooking: Indian, Chinese, African and Western cooking.Their results showed very low sensitivity of CMB to the different cooking proles applied, despite the difference in the source proles.This may explain the less satisfactory correlation of POC ck estimated by the 3 methods.Cooking was also reported as one of the most difficult sources to characterize in receptor modelling. 46The correlation of POC ck estimated using all three methods at IAP and PG during winter and summer was also investigated (Fig. S4 †).No obvious correlation was observed, except at IAP in winter for the EG method and AMS-PMF, suggesting a large uncertainty in estimating POC ck .
3.3.4Primary OC from non-fossil sources (POC nf ).The correlations of POC nf estimated by the three methods were also investigated (Fig. S5 †).In the CMB results, POC nf is the sum of vegetative detritus, biomass burning and cooking.For the EG method and AMS/ACSM-PMF, POC nf is the sum of POC bb and POC ck .The correlation between CMB and AMS/ACSM-PMF was good with r 2 of 0.83 and slope of 1.1.But the correlation between the EG method and the other two methods was not very good with r 2 of 0.50-0.55 and slopes of 0.73-1.56.Uncertainties within the apportionments of POC bb and POC ck by the three methods make it difficult to quantify total non-fossil POC.
3.3.5Secondary OC from all sources (SOC).The SOC estimated by AMS/ ACSM-PMF was poorly correlated with that estimated by the other two methods (Fig. 6).However, the SOC estimated by the EG method and the other OC estimated by CMB were better correlated with r 2 of 0.72 and slope of 1.54.The correlation results for SOC estimated using all three methods at IAP and PG during winter and summer are provided in Fig. S6.† The SOC concentrations for the three methods correlated well with each other (r 2 > 0.8) in summer at IAP and PG, with slopes ranging between 1.09 and 1.44.In winter, AMS/ACSM-PMF generally correlated well with the other two methods (Fig. S6 †), but the absolute concentrations varied appreciably.

Source apportionment of PM 2.5
The PM 2.5 source apportionment results from PMF, CMB and AMS/ACSM-PMF were compared for samples collected on identical days (Table 3).It should be noted that PMF modelling was conducted based on lter-based data from 133 samples at both sites during winter and summer (Table S4 †) but a comparison was only made for the dates when data was available for all methods.To reconstruct PM 2.5 using the OC source apportionment results obtained by CMB, the source contributions were calculated using the source-specic OC concentration multiplied by the OC/PM 2.5 ratio in the corresponding source prole; more details can be found elsewhere. 36In addition, dust and SNA (sum of measured sulfate, nitrate and ammonium) were also added; dust (geological minerals) was calculated by eqn (1) below, 53 and for AMS/ACSM-PMF, SNA is the non-refractory sulfate, nitrate and ammonium in NR-PM 1.0 .Geological minerals ¼ 2.2Al + 2.49Si + 1.63Ca + 1.94Ti + 2.42Fe As shown in Table 3, the measured concentrations of SNA at IAP were higher than those of the corresponding factor in PMF, but they were comparable at PG.The SNA concentration in the AMS data was much higher than the measured SNA concentration during winter, but lower than that in summer at IAP. Differences were also found between online ACSM and lter-based SNA concentrations in another study. 54Possible reasons could be the uncertainties of SNA in ACSM analysis, 55 and the evaporation of ammonium nitrate and the difficulties in separating organosulfate from sulfate in AMS. 56The lower average SNA concentration in PMF is probably due to the contribution of the secondary inorganics factor being zero in some samples, as computed by PMF.The dust concentration in PMF was around 2-3 times that estimated in the CMB results, suggesting that one of the PMF dust factors is misassigned.
For organics, PMF was unable to resolve either cooking or secondary sources.For coal combustion, the estimates were comparable for both CMB and PMF results in winter.But in summer, the concentration for CMB was higher than that in the PMF results.It is difficult for PMF to resolve different factors (both offline and online) when the concentrations are relatively low.However, CMB appears to be more sensitive in resolving different sources in low concentration PM samples.As the coal combustion factor was resolved by all methods at both sites during   The source contribution is marked as "0.0 AE 0.0" when it is too low to be identied as a single factor in AMS/ACSM-PMF.c "N.D." means no data available.d Sum is the sum of all sources listed in the table and additional sources: for CMB, sum also includes vegetative detritus; for AMS/ACSM-PMF, it also includes NR-Cl À .
winter, the time series and correlations at IAP and PG are provided in Fig. S7 and S8, † respectively.Generally good correlation (r 2 > 0.7) was only found between CMB and AMS/ACSM-PMF at both sites, but the concentrations were somewhat different.
The time series of biomass burning aerosols at both sites estimated by all 3 methods followed a similar trend (Fig. S9 and S10 †).Moderately good correlations of the 3 methods were found at PG, but the concentrations varied.Biomass burning is a signicant factor in PMF, which resulted in over 30 mg m À3 of BBrelated PM 2.5 in winter at both sites.This is much higher than the BB aerosol concentrations estimated by CMB and AMS/ACSM-PMF.A comparative analysis of applications of PMF to multi-constituent chemical datasets from Beijing has demonstrated the inconsistency of their ndings and the problematic nature of the application of this method to Beijing aerosols, 41 consistent with the ndings of this study.In summer, the BB-related PM 2.5 concentrations estimated by CMB were 0.8 and 2.7 mg m À3 at IAP and PG, respectively.However, those estimated by PMF were only 0.5 and 0.1 mg m À3 at IAP and PG, respectively.PG is a rural site, where BB is used for cooking and heating.This is shown in the results from both the 14 C/EG method and CMB.Hence, PMF probably did not successfully resolve BB emissions.
The average concentrations of traffic related particles were generally low and comparable for the different methods in summer, but with no correlation of the time series and concentrations (Fig. S11 †).In winter, the concentrations of traffic particles are comparable for CMB (6.1 AE 5.3 mg m À3 ) and PMF (7.1 AE 6.7 mg m À3 ) at IAP but no obvious correlation is observed (Fig. S12 †); those estimated by CMB (16.3 AE 11.6 mg m À3 ) and ACSM-PMF (9.4 AE 7.3 mg m À3 ) at PG were much higher than that estimated by PMF (3.8 AE 3.5 mg m À3 ), but the time series are well correlated (Fig. S13 †).
Cooking emissions were only resolved by CMB and AMS/ACSM-PMF.At the IAP site, the cooking OA (COA) concentrations estimated by CMB are about half those estimated by AMS-PMF during both seasons, which is consistent with other studies which reported that COA was overestimated around 2-fold by AMS-PMF. 4,46The COA concentration at PG was much higher in the ACSM-PMF results (6.6 AE 3.6 mg m À3 ) than for CMB (0.8 AE 0.7 mg m À3 ), suggesting other inuences on one or the other method.
Overall, the CMB source apportionment results appear more representative of reality based on the intercomparison and correlation analysis.From the CMB modelling results, the major sources of PM 2.5 in Beijing were secondary inorganic ions, secondary organic aerosols, primary coal combustion and biomass burning emissions.The relative abundance of source contributions (%) in the CMB results at IAP and PG during haze and non-haze days was also investigated (Table S6 †).SNA increased signicantly during haze days, especially on the haze day (27 th May 2017) in summer.This is consistent with secondary inorganic aerosol formation making a major contribution to haze formation in Beijing.Liu et al. (2019) 57 applied PMF for PM 2.5 source apportionment of online data recorded in urban Beijing (Peking University, PKU) with 1 h time resolution during the same winter campaign and resolved 6 sources including dust, coal, industry, traffic, biomass and secondary sources.The contribution from combined coal and industry sources to PM 2.5 for PMF at PKU was comparable with that from combined industrial and residential coal combustion for CMB at IAP (Table S6 †) during haze (22-24%) and non-haze days (20-21%).The contributions from biomass burning, dust and traffic emissions to PM 2.5 were higher on non-haze days in both studies.But the percentages of biomass burning and traffic were generally much higher for PMF-PKU than CMB, especially on non-haze days.While secondary particles (SNA + secondary OM) during haze and non-haze days were higher for CMB (52% and 45%) than for PMF-PKU (44% and 21%).This is probably because the secondary organic sources were not very well separated in PMF as mentioned earlier.

Summary
The 14 C/extended Gelencsér (EG) method, PMF, CMB and AMS/ACSM-PMF were used for the source apportionment of OC, EC and PM 2.5 at urban and rural sites in Beijing during winter and summer.The results from these methods were intercompared and evaluated through correlation analysis.The results of the OC source apportionment intercomparison are summarized here: (1) The reconstructed OC from all apportioned sources was comparable for CMB, the EG method and AMS/ACSM-PMF, but lower for PMF, which is due to the inability of PMF to model heavily polluted events and separate POC and SOC.
(2) CMB, the EG method and AMS/ACSM-PMF provide a consistent apportionment of POC f in haze samples.CMB and the EG method are consistent in separating OC into POC f , POC nf and SOC in non-haze samples, but the AMS/ ACSM-PMF and PMF methods are not.
(3) For fossil fuel sources, a strong correlation was found between CMB and both the EG method and AMS/ACSM-PMF for POC f .Coal combustion POC (POC cc ) and traffic POC (POC tra ) were also correlated for CMB and AMS/ACSM-PMF, with slopes close to 1.
(4) For non-fossil fuel sources, the correlation of POC nf estimated by CMB and AMS/ACSM-PMF was good with r 2 of 0.83 and a slope of 1.1, while the correlation of the POC nf estimated by the EG method with that estimated by CMB and AMS/ ACSM-PMF was not very good.The POC bb concentrations provided by CMB and AMS/ACSM-PMF were more comparable.The POC ck concentrations were less correlated for the three methods, suggesting large uncertainty in estimating POC ck .
Receptor modelling of PM 2.5 in Beijing showed that it arises mainly from secondary inorganic and organic aerosols, primary coal combustion and biomass burning emissions.The PM 2.5 source apportionment intercomparison shows that: (1) For coal combustion, the time series of CMB and AMS/ACSM-PMF correlated well.Comparable concentration levels were only found for CMB and PMF in the winter.
(2) For biomass burning, the time series of CMB, PMF and AMS/ACSM-PMF correlated well, but the concentrations are only comparable at IAP during winter.The PMF results were problematic as biomass burning emissions are heavily overestimated.
(3) The average concentrations of traffic related particles were generally comparable for the different methods except at PG during winter.
(4) The cooking aerosol estimates by AMS/ACSM-PMF and CMB varied signicantly.The secondary OM concentrations were comparable for CMB and AMS/ACSM-PMF at IAP, but those at PG differed signicantly.PMF did not resolve either cooking or secondary sources.
(5) The measured SNA concentration at IAP was higher than the SNA factor in PMF, but they were comparable at PG.The dust concentration in PMF was around 2-3 times that estimated in the CMB results, suggesting that at least one of the PMF dust factors is misassigned.
Our intercomparison exercise suggests that although there are some consistencies, the contributions of several sources modelled by CMB, PMF and AMS/ ACSM-PMF differed signicantly.The results from the CMB model appear to be both comprehensive and most consistent with those from other methods, whereas PMF did not work well with the APHH-Beijing dataset.

Fig. 1
Fig. 1 Source contributions to OC in winter (blue-shaded) and summer (pink-shaded) at the IAP and PG sites by CMB, PMF and AMS/ACSM-PMF (note: the reconstructed OC in the middle of the pie chart is the sum of the OC from each source; VD: vegetative detritus; BB: biomass burning; CC: coal combustion; OOC: oxidized OC; CCOC: coal combustion OC; BBOC: biomass burning OC; COC: cooking OC; HOC: hydrocarbon-like (traffic) OC).

Table 2
Comparison of OC source apportionment results (mg m À3) obtained using different methods in winter and summer for the IAP and PG sites in Beijing (only

Table 2 (
Contd. ) a "-" means the method could not resolve the corresponding source.b Maximum value for traffic related POC (POC tra ), which is calculated by multiplying EC f by the OC/EC ratio for primary traffic emissions (0.85 AE 0.16) in China, 44 assuming that EC f only originates from traffic emissions.c Minimum value for coal combustion related POC, which is calculated by subtracting the maximum POC tra from POC f .d "N.D." means no data available.

Table 3
Comparison of PM 2.5 source apportionment results (mg m À3 ) obtained using different methods in winter and summer at the IAP and PG sites in Beijing Open Access Article.Published on 23 September 2020.Downloaded on 11/10/2023 6:32:40 AM.This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Table 3 (
Contd. ) a "-" means the method could not resolve the corresponding source.b